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Estimacin deductiva Evidencia interna Comparacin con la fuente R: :Pi    8 8 o Siete pasos  Determinar si se requiere exactitud horizontal, vertical o ambas Seleccionar un conjunto de test points Identificar y extraer los homlogos de un conjunto independiente de mejor exactitud Tomar medidas en puntos idnticos a los anteriores.nZhT3 )Datos independientes?$ Buscar puntos comunes Exactitud Idealmente >> triple En otro caso& lo que haya (si es mejor!) Documentarla en metadatos Usar slo cifras significativas! Exactitud ~uniforme en rea rea ~equivalente<!Z@ZjZ!@j</ M  8 8!mSiete pasos (cont) Calcular un estadstico de la exactitud de la posicin segn corresponda Preparar la declaracin de exactitud segn el formulario Incluya esa declaracin en los metadatos$nIb *.Clculos en horizontal&  8,0Clculos en la vertical&  8_!Variables temticas o categricas! No contempladas en el NSSDA Es importante hacer foco en: Naturaleza de los errores Se confundieron especies de pinos? Se confundi trigo con vid? Frecuencia de los errores Magnitud de los errores Origen de los erroresdZZZAZHZ9AH aCmo medir la Exactitud? Prepare una matriz de confusin Elija N puntos al azar Vea lo que dicen los datos Vea lo que hay en el terreno Cuente los casos Idealmente, todo en la diagonalB `  `! bAlguna terminologa 8Error por Omisin Def.: Error por columna/total en columna (1.0 - Exactitud del productor) Error por Comisin Def: Error por fila/total en fila (1.0-Exactitud del usuario) No incluir los elementos de la diagonal! IA+: 4 *( 8) 8cResultados del ejemplo 8Exactitud Total: (10+20+10)/(10+2+3+0+20+0+4+1+10)= 40/50 = 80% Exactitud de comisin para la clase A: 10/(10+2+3) = 10/15 = 67% Exactitud de omisin para la clase A: 10/(10+0+4) = 10/14 = 71% R ?9,D 1    dLa tabla completa 8eEl ndice kappa de Cohen$   8Una medida de la exactitud observada en comparacin con el azar Es un nico nmero (un escalar) El ideal sera 1.0; lo peor sera 0.0 Un valor intermedio 0.83 implica que se estn evitando 83% de los errores que cometera una clasificacin al azar No est recogido en los estndares Sin embargo se usa& Cmo calcularlo?AA _  fEjemplo: Calcular  q para cada caso Def.: q es el nmero de casos en la diagonal por puro azar qi=sumi(fila)* sumi(col)/N tnZWZ<  r gEjemplo (cont.): .Calcular kappa Def.: kappa=(traza(A)-q)/(N-q) Ln  . h(Un pequeo problema&  Se asume que no hay confusin posible al construir la matriz de confusin En la prctica& Absolutamente incorrecto Comprensible, pero incorrecto Razonable, pero podra ser mejor Buena respuesta Absolutamente correcto jZZZZZZZ C8Digresin: Midiendo Calidad&  Estamos revisando los siete pasos Hemos visto algunos tests de Exactitud Algunos estandarizados, otros no Para posicin Para atributos Esencialmente controlan Exactitud Pero en Calidad no todo es Exactitud& 6jIjI i$Otras componentes&  ACompletitud Coherencia lgica Exactitud temporal Linaje MetadatosA "jEjemplo: Coherencia lgica Representacin sin sentido Caminos en el agua Isolneas que se cortan Puentes sin rutas o sin ro Cuencas hidrogrficas vs. ros 2fg #k8Volviendo a los Siete pasos&  Calcular un estadstico de la exactitud de la posicin segn corresponda Preparar la declaracin de exactitud segn el formulario Incluya esa declaracin en los metadatos,nI9) +Declaracin de Exactitud 8En el estndar se consideran dos formatos:  __ mts de exactitud (horizontal/vertical) al 95% de confianza  Compilado para tener __ mts de exactitud (horizontal/vertical) al 95% de confianza Usar (1) si se dispone de datos especficos independientes Usar (2) si se utiliz un procedimiento estndar consistente con el error obtenidoF++N 8FIncluyendo la Incertidumbre Falacia de Falsa Precisin Una represa de 1:234.567,89 m3 La probabilidad de falla es 0.3579 Regla (indefendible& ): un dcimo de la resolucin Poblacin en unidadesdensidad en dcimos Simple y popular, pero errnea!B2K #25<  8  8GIncluyendo Incertidumbre(2)$ *Falacia de Falsa Certidumbre Respuestas  precisas sin sustento Exacerbado al combinar capas Ni hablar de mezclar escalas Problema extremadamente corriente Lo correcto sera alguno de: resultado+intervalo [peor, tpico, mejor] [min,max] con probabilidad X Cmo determinarlo? vG G  8 $pSiete pasos (cont) Calcular un estadstico de la exactitud de la posicin segn corresponda Preparar la declaracin de exactitud segn el formulario Incluya esa declaracin en los metadatos$n) -Comunicando&   8Si hay varias capas, podra requerirse una declaracin para cada una de ella Si hay una mezcla inseparable y no ensayada, asignarle el peor nivel de error Si est ensayada, asignarle el nivel obtenido Nunca use ms cifras que las de los datos  8E0Otras formas de estimar&  8Si tiene pocos puntos Si la distribucin es claramente no-gaussiana No est previsto en el estndar! Use Remuestreo (Bootstrap)Bff  D 8? 8MFPorqu Remuestrear?  En ocasiones no es posible tener muchas muestras de una poblacin En ocasiones no es correcto (o posible) asumir una distribucin para una poblacin El objetivo es: Assess sampling variation$G Bootstrap Efron (biostadstico de Stanford ) a finales de los 80 s  Pulling oneself up by one s bootstraps Es un enfoque no paramtrico para inferencia estadstica Usa clculos (fuerza bruta) en lugar de resultados asintticos e hiptesis tradicionales sobre distribuciones Puede usarse para obtener errores estndar, intervalos de confidencia y prueba de hiptesis R9)9)=\  *HEjemplotAdaptado de Fox (1997)  Applied Regression Analysis Objetivo: Estimar diferencia promedio de respuestas entre Hombre y Mujer Se dispone nicamente de cuatro parejas de observaciones: ~* WIJDiferencia promedio4Promedio de la muestra es (6-3+5+3)/4 = 2.75 T     $! KEstimadores corrientesEl estimador de s es El estimador de la desviacin estndar es Asumiendo que la poblacin es normal, podemos usar la distribucin-t comofv`a`+J    +LIntervalo de Confianza CI= m = 2.75 4.30 (2.015) = 2.75 8.66 -5.91 < m < 11.41\>' a $7MMedia y varianza de la muestraIdea: usar la distribucin Y* de la muestra para estimar la distribucin Y de la poblacin y* p*(y*) 6 .25 -3 .25 E*(Y*) = S y* p(y*) = 2.75 5 .25 V*(Y*) = S [y*-E*]2p(y*) 3 .25 = 12.187 DE*(Y*)=sqrt(V*(Y*) )=1.745[ZZZ\   =     m   NMuestreo con Reemplazo$  OCalculando nuevos CI El promedio de estos 256 promedios es nuevamente 2.75, pero su desviacin es ahora (sin  ^ porque la desviacin ahora no se estima) TT" 1"   (P Y entonces?  Esto ya era sabido! Pero mediante remuestreo o bootstrap Los Intervalos de Confianza pueden ser ms precisos Pueden ser calculados para problemas no lineales que no tienen frmulas de error conocidasF%%H 3ZQJLa poblacin es a la muestra lo mismo que la muestra es a las remuestrasKK$JR Procedimiento 1. Especifique un criterio de muestreo que produzca la muestra que se utilizar Criterio(poblacin) muestra4qd TM 8 SProcedimiento(2)  83. Para cada remuestra, calcule el estimador estadstico de su inters 4. Use la distribucin de los estimadores de las remuestras para estimar las propiedades de la muestra d : OX Atencin:  8Remuetreo no es vlido absolutamente para todo No debe usarse si hay colas  largas Ej.: estimacin del rango :n Jn 8Y Otro ejemplo:  8Ver si unos datos ajustan al modelo Confirmar que el proceso est bajo control Tomar muestras al azar y confirmar que es de distribucin, parmetros y escala fijos En particular, confirmar CI al 95%d%+U#& U# 8 ZQu hacer primero? 4 grficos(  [(Supongamos Uniforme&   \Un estimador para C Yi no es normal Aplicaremos remuestreo Estimadores posibles de C Media Mediana Promedio del rango Quiz otros& Buscaremos el de mnima varianzaNAZ.Z!Z?.!  ]Cmo lucen los CI  ^Importancia&   8Lo tpico es requerir CI para la media Caso normal: hay solucin analtica En otros casos no la hay Es donde el bootstrap/resampling muestra su importanciaT'$8' $ 8  8WOtros mtodos de remuestreoJackknife (sacar de a uno) es un caso especial de bootstrap Remuestreo sin un caso y sin reemplazo (las muestras pasan a tener tamao n-1) Validacin cruzada Divide los datos en entrenamiento y test Generalmente se los usa para estimar intervalos de confianza en predicciones para el modelo  full (i.e., modelo que usa todos los casos)<O) #J)l  &  (  DRecapitulando: Vimos estndares Vimos mtricas de Exactitud Posicionales Atributos Cuantitativos, Cualitativos, etc Vimos mtodos para medir Exactitud Cuando hay acceso a suficientes valores mejores Cuando son gaussianos Para los otros casos Explicamos e ilustramos Bootstrap Mencionamos Jacknife-Z8Z#ZFZZ7Z-8#  7   %qPlan  ~Error, Exactitud y Precisin Definiendo estndares Informando sobre la Calidad Midiendo y Verificando Anlisis de Sensibilidad"f4@    L Anlisis de Sensibilidad 8Siempre hay que Validar los resultados Conjunto de entrenamiento Conjunto de validacin Cmo? Depende del Modelo+Datos Datos continuosderivada parcial Datos categricossimulacin Se suele hacer al final& pero puede invalidar todo el proyecto!h'Z1Z^ZAZ'1/H'( 8& 8&Cuanto antes mejor&  8Si el dato no existe con la exactitud requerida Si no era necesaria tanta exactitud Todo cuesta! Datos pueden ser irrelevantes& Tipo de suelo para estudio elico Relevancia diferente segn el output Produccin de energa en kWh-ao Costo del proyecto en U$S pT"%<b"%< @T 8 8  8"Ejemplo analtico 1 JSupongamos Cmo se relaciona la Var(f) con Var(x)? Ms en general: KKH& #Ejemplo analtico 2 Consideremos ahora$Otras frmulas analticas  HAhora considrese Resultados similares para Otras frmulas tiles<~   .En general&   8[Hay que estimar las derivadas parciales Mtodos numricos aproximados: Cociente incremental<GZZ:  \ 80 Derivada exacta&  8Derivacin manual Slo en casos simples; require codificar Derivacin automtica Variante 1: Generador de nuevo cdigo Variante 2: Sobrecarga de operadores Paquetes ADOL-F/ADOL-C TAPENADE Matlab+ADMAT Otros& Ejemplos)K + )K +  81Generadores de cdigo 8Generan automticamente un segundo cdigo fuente a partir del disponible ADOL-C/ADOL-F/TAPENADE, etc. Derivada exacta; no hay cociente incremental Ejemplo:P 8/Sobrecarga de operadores 8BSlo en ambientes orientados a objetos Ej.: Matlab + ADMAT toolbox C 8HEn qu andbamos? Estbamos haciendo un Anlisis de Sensibilidad Alcanza/no alcanza la Exactitud de los datos disponibles? Vimos Mtodos Analticos Slo para datos continuos Veremos mtodos Estadsticos de Simulacin Para datos continuos/categricos/;,!/ ; , !    Mtodos de Monte Carlo Cualquier procedimiento que usa nmeros aleatorios Nmeros aleatorios? Qu es un nmero aleatorio? Un nmero? Secuencia de nmeros aleatorios RHIH$  ) $ ,x&La parte aleatoria&  VDistribucin Uniforme Todo nmero en [0,1] tiene la misma probabilidad Fundamental (se usa para otras distribuciones) Para muestreo al azar, etc. Cmo generar una secuencia de nmeros aleatorios? Usar un sistema catico (moneda, dado, etc.) Usar un proceso inherentemente randmico Usar tablas de nmeros aleatorios Problema: Resultados no reproducibles Imprctico, no confiable (sesgos?) Tablas  no suficientemente extensasZ|Z3ZxZ ZeZ|3x d     -yNmeros seudo-aleatorios yNmeros pseudo-aleatorios generados con algoritmos No correlacionados, ciclos largos, etc. Ej.: Middle square algorithm (J. Von Neumann, 1946): Para generar una secuencia de enteros de 10 dgitos: Elija uno cualquiera, Elvelo al cuadrado y luego Extraiga los 10 dgitos intermedios como el siguiente nmero de la secuencia Por ejemplo: 3690295441 136182804418653844813P(P5P5PPPPPP3(55 03'  .z"Seudo-Aleatorios&  No son al azar! Son series totalmente determinsticas y predecibles Lucen como al azar, pero & $aP _ /|)Linear congruential method (Lehmer, 1948)** ,  fIn+1 = (a*In + c) mod m I0 = Valor inicial (semilla) a,c e" 0, m > I0 , a,c Una mala eleccin de constantes generar secuencias malas: Ej.: a=c=I0=7, m=10 7,6,9,0,7,6,9,0,... Z5Z;Z+ZZ   ;         ;  '0} Familia popular&  RANDU: In+1 = (65539*In) mod 231 Se vio que no era bueno RANMAR: In = (a*In-1 + b*In-2) mod m genera series con perodo@ 1043 En general se deberan usar generadores conocidos, con propiedades bien documentadas Sin embargo& !ZZ%Z ZcZ  b<  Eb 1~Para PDFs no uniformes Puede haber rutinas especficas (ej.: N(0,1)) Otros casos? Mtodo de la probabilidad inversa Calcular Generar t~U(0,1) Evaluar x resulta tener pdf igual a f(s) Hay otros mtodos para casos particulares Problemas: pdf s discretas, eficiencia, etc.=" ;*-=" ; *-(s =K 82Simulacin de Monte Carlo  8 Aparece con las primeras computadoras (1945-55) reas de aplicacin incluyen biologa, qumica, informtica, anlisis de datos economtricos y financieros, ingeniera, ciencia de los materiales, fsica, ciencias sociales, estadstica, etc. La SMC se resume en: Asumiendo un mecanismo para generar datos de su proceso Produzca nuevas instancias de datos simulados Examine estadsticamente los resultados de esas instancias Si se tiene  la pdfSMC estndar Si no, se usa Remuestreo (que es un pariente cercano)pZZXZ86|0 /b-   85 J$Algunos problemas&  SMC plantea gran demanda de CPU Varianza ~1/sqrt(N) Bajar el error un 10% requiere multiplicar por 100 el nmero de simulaciones Se intenta mejorar esta caracterstica Tcnicas de Reduccin de Varianza (TRV) Veamos de qu se trata& ` a'( a'(<) B< 8A 8>TRV: Enfoque Antittico 8?Ejemplo: Integral (o promedio) 8@"Cmo lograr correlacin negativa?##(" AOtros trucos&   Si se quiere calcular !Aspectos importantes en SMC Diseo apropiado Medida de la exactitud del resultado Justificacin del nmero de casos/muestras Seleccin del generador aleatorio Memoria y tiempo de clculo Tcnica de reduccin de varianza Software usado Anlisis del resultado (visualizacin, ajuste por curvas, etc.)Z K En resumen:  Como productor: hay estndares para expresar Exactitud Para posicin y variables continuas No para variables categricas Estimacin basada en suficientes valores ms exactos Alternativamente, usar Bootstrap Como usuario: preocuparse mucho slo si el problema es sensible 7ZBZ5Z!Z@ZZ7B   !   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(O___PPT10+^D|' = @B D7' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*+V   pP(  pr p S 4rH Yp`  H   p S 0sH  Ypv<$ 0 H  H p 0޽h ? @@>6___PPT10.c@)q5+翷D' = @B Dm' = @BA?%,( < +O%,( < +D' =%(D' =%(D:' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p-%(D' =-i6B wedge*<3<*p-D' =%(D' =%(D:' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p-A%(D' =-i6B wedge*<3<*p-AD' =%(D' =%(D:' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*pAU%(D' =-i6B wedge*<3<*pAUD' =%(D' =%(D:' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*pUq%(D' =-i6B wedge*<3<*pUqD' =%(D' =%(D:' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*pq%(D' =-i6B wedge*<3<*pqD' =%(D' =%(D:' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =-i6B wedge*<3<*p+8+0+pH  +-  0( t(  tr t S  H Yp`  H   t S H  YpP<$  0 H  h t  fH xaxa 1?"6@`NNN?N  Fuente: Foote and Huebner 4( nK2  H t 0޽h ? @@u*m*___PPT10M*.c窂+fJ(D)' = @B D)' = @BA?%,( < +O%,( < +D' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*t)%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*t)D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*t)D' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*t)O%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*t)OD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*t)OD' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*tOe%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*tOeD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*tOeD' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*te%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*teD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*teD' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*tD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*tD' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*tD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*tD' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*tD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*tD' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*tD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*tD' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*tD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*t+8+0+tH  +   x\(  xx x c $dH Yp`  H   x c $`H  Ypv<$ 0 H  H x 0޽h ? @@___PPT10.c窂+{/D6' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-6B#slide(fromRight)*<3<*xD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*x-%(D' =-6B#slide(fromRight)*<3<*x-D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*x-C%(D' =-6B#slide(fromRight)*<3<*x-CD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*xCg%(D' =-6B#slide(fromRight)*<3<*xCgD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*xg%(D' =-6B#slide(fromRight)*<3<*xgD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-6B#slide(fromRight)*<3<*x+8+0+xH  +   |P(  |r | S DH Yp`  H   | S @H  Y0v<$ 0 H  H | 0޽h ? @@jb___PPT10B.d0Gd+ D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =-o6Bdissolve*<3<*|D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*|=%(D' =-o6Bdissolve*<3<*|=D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*|=\%(D' =-o6Bdissolve*<3<*|=\D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*|\}%(D' =-o6Bdissolve*<3<*|\}D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*|~%(D' =-o6Bdissolve*<3<*|~+8+0+|H  +6  ph (     x0e0eA>5%j0302827l <$@  0 H r  S (H Yp`  H    c $H  Y`v<$ 0 H    S xaxa0W>d?f P 6No sea complaciente! Impact"6@ NNN?N ,$D  0H  0޽h ? @@11___PPT101.d#+2qD/1' = @B D0' = @BA?%,( < +O%,( < +D' =%(D' =%(Dm' =A@BB#BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =+4 8?HCB4DBCBB*k3>'Bstyle.rotation<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =%(D' =%(Dm' =A@BB#BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-g6B fade*<3<*0D' =+4 8?HCB4DBCBB*k3>'Bstyle.rotation<*0D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*0D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*0D' =%(D' =%(Dm' =A@BB#BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0;%(D' =-g6B fade*<3<*0;D' =+4 8?HCB4DBCBB*k3>'Bstyle.rotation<*0;D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*0;D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*0;D' =%(D' =%(Dm' =A@BB#BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*;D%(D' =-g6B fade*<3<*;DD' =+4 8?HCB4DBCBB*k3>'Bstyle.rotation<*;DD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*;DD' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*;DD' =%(D' =%(Dm' =A@BB#BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*DO%(D' =-g6B fade*<3<*DOD' =+4 8?HCB4DBCBB*k3>'Bstyle.rotation<*DOD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*DOD' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*DOD' =%(D' =%(Dm' =A@BB#BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Of%(D' =-g6B fade*<3<*OfD' =+4 8?HCB4DBCBB*k3>'Bstyle.rotation<*OfD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*OfD' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*OfD' =%(D' =%(Dm' =A@BB#BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*fs%(D' =-g6B fade*<3<*fsD' =+4 8?HCB4DBCBB*k3>'Bstyle.rotation<*fsD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*fsD' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*fsD' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*+8+0+H  +6 ZK0 00$$t,0(  t t S ~H xaxa1 ?Yp`  H   t S ~H xaxa1 ? Ypv H  @.  /  t#  ,$D 0" t c BC DEFb1?,,N4.yl P6A'y ;IWA?|e*Ksl 9) MNY\@- : t c BC*DE<FDA1?tE  "D)_)v( @  . t c BCDEFb!1?""+IcnnzpiyWGv6eD|RyK7.$+  A]0wPEH@ z t c JB CDE\FdA@1?%9 _1rN|[gnRB6*" h 5%/0@* Y3 z  t c JB4CDE\FdA@1? 5 [?sfvyfY)R3F.;!, qSF8 /0@   t c ZB<CDEdFlA@1?<8m`t;_7U-G2)%%&,*S1!34@ ;Z  t c *BCDELFTA@1?\mc.v[K=&8a\'(@(K   t c BCIDEF$___1?H@X  t c BC}DEF?1? & <L*_^{g|m|z /H,gQl|u\5WCAD@   t c B@C~DEFb1?''m%#  P"5F+Zju?R'nGg{}x9o=`>W?N4$em%OP@  2 t c BCJDEFA1?.. 5Da}|\'CID3%g R<iUJDP]_]XXJ)%7 Z&% )1:j8d ]`@&g p t c BCDEFq1?&& o f \ K B 8   *#8yA?4'5Fh&N|j.,MP@ ( * t c B[C2DE4F<1? F2 " .151A1S+ZDF@$ 9z t c JBCwDE\FdA1?n Y 9 9Y l-vHufqieedh /0@ / uJ t c BC|DEDFLq1?|Je{twblDV% )7%fAzJ|J#$@F1  t c B8C+DEF$1?2*7 $2*@5  t c ZBCgDEdFlq1?/+k,S(- -/>PVdbtfx`zWF80/34@ ' t c BCTDE|Fq1? m!Y)O,E,%  #+1(<JL]RgSoSsNrDr;v4. ?@@" v t c jBCXDElFtq1?  [ M+I0A0"&# "")6C L5V?WLUQQQLQFU?& 78@; j  t c ZBC(DEdFlq1?}[K?" &3&=&I't&%$$$%& 34@Z . ?  t c BCC-DE$F,1? , .? B)",@   t c B<C*DE,F41? # )8 ;$!% )#@ - W t c B1C,DE(F01? +"(0 & +@ m0 `B t 01? `B t 0OOO1?; t c BSC_DEF?1?""RR]@z=f=]=S=X\^^lD ),5E#:BCC1'*2=D L  (5REH@ - 2 t c BC-DE8F@A1?H ?* ,*?,V* @ ;R  t c "BC+DEHFPA1? p ` U@6'1(E*]&%(@ ] Z !t c *BC<DELFTA1?kX E:/-%,-(2%40;#;/;F5 '(@g   "t s BNCXDE F(@1?MWS6+?MIk2@ , X #t s (B0CDEHFP@1?/p?lA&U%(@,  $t c RBC6DE`FhA1?k[TLE:%  /4(534R%Zh/x%w  14@E  H t 0޽h ? (O___PPT10+^D|' = @B D7' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*tD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*t+62   P(  r  S H Yp`  H    S H  Yp<$ 0 H  H  0޽h ? @@00___PPT10/.e`>+o%D/' = @B DM/' = @BA?%,( < +O%,( < +D$' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*D' =-g6B fade*<3<*D$' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*8D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*8D' =-g6B fade*<3<*8D$' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8L%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*8LD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*8LD' =-g6B fade*<3<*8LD$' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Lh%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*LhD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*LhD' =-g6B fade*<3<*LhD$' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*hD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*hD' =-g6B fade*<3<*hD$' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*D' =-g6B fade*<3<*D$' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*D' =-g6B fade*<3<*D$' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*D' =-g6B fade*<3<*D$' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*D' =-g6B fade*<3<*+8+0+H  +6 ZK0 00$$x,0(  x x S ~H xaxa1 ?Yp`  H   x S ~H xaxa1 ? Ypv H  @.  /  x# ` pm ,$D 0" x c BC DEFb1?,,N4.yl P6A'y ;IWA?|e*Ksl 9) MNY\@- : x c BC*DE<FDA1?tE  "D)_)v( @  . x c BCDEFb!1?""+IcnnzpiyWGv6eD|RyK7.$+  A]0wPEH@ z x c JB CDE\FdA@1?%9 _1rN|[gnRB6*" h 5%/0@* Y3 z  x c JB4CDE\FdA@1? 5 [?sfvyfY)R3F.;!, qSF8 /0@   x c ZB<CDEdFlA@1?<8m`t;_7U-G2)%%&,*S1!34@ ;Z  x c *BCDELFTA@1?\mc.v[K=&8a\'(@(K   x c BCIDEF$___1?H@X  x c BC}DEF?1? & <L*_^{g|m|z /H,gQl|u\5WCAD@   x c B@C~DEFb1?''m%#  P"5F+Zju?R'nGg{}x9o=`>W?N4$em%OP@  2 x c BCJDEFA1?.. 5Da}|\'CID3%g R<iUJDP]_]XXJ)%7 Z&% )1:j8d ]`@&g p x c BCDEFq1?&& o f \ K B 8   *#8yA?4'5Fh&N|j.,MP@ ( * x c B[C2DE4F<1? F2 " .151A1S+ZDF@$ 9z x c JBCwDE\FdA1?n Y 9 9Y l-vHufqieedh /0@ / uJ x c BC|DEDFLq1?|Je{twblDV% )7%fAzJ|J#$@F1  x c B8C+DEF$1?2*7 $2*@5  x c ZBCgDEdFlq1?/+k,S(- -/>PVdbtfx`zWF80/34@ ' x c BCTDE|Fq1? m!Y)O,E,%  #+1(<JL]RgSoSsNrDr;v4. ?@@" v x c jBCXDElFtq1?  [ M+I0A0"&# "")6C L5V?WLUQQQLQFU?& 78@; j  x c ZBC(DEdFlq1?}[K?" &3&=&I't&%$$$%& 34@Z . ?  x c BCC-DE$F,1? , .? B)",@   x c B<C*DE,F41? # )8 ;$!% )#@ - W x c B1C,DE(F01? +"(0 & +@ m0 `B x 01? `B x 0OOO1?; x c BSC_DEF?1?""RR]@z=f=]=S=X\^^lD ),5E#:BCC1'*2=D L  (5REH@ - 2 x c BC-DE8F@A1?H ?* ,*?,V* @ ;R  x c "BC+DEHFPA1? p ` U@6'1(E*]&%(@ ] Z !x c *BC<DELFTA1?kX E:/-%,-(2%40;#;/;F5 '(@g   "x s BNCXDE F(@1?MWS6+?MIk2@ , X #x s (B0CDEHFP@1?/p?lA&U%(@,  $x c RBC6DE`FhA1?k[TLE:%  /4(534R%Zh/x%w  14@E  H x 0޽h ? (O___PPT10+^D|' = @B D7' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*xD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*x+   P(  r  S |CYp`  C   S xC Ypv<$ 0 C H  0޽h ? @@___PPT10.e`53+$MDV' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B+checkerboard(across)*<3<*D' =%(D' =%(DX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*3%(D' =-6B+checkerboard(across)*<3<*3D' =%(D' =%(DX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*3e%(D' =-6B+checkerboard(across)*<3<*3eD' =%(D' =%(DX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*e%(D' =-6B+checkerboard(across)*<3<*eD' =%(D' =%(DX' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B+checkerboard(across)*<3<*+8+0+C +R5  P(  r  S CYp`  C   S CY`<$ 0 C H  0޽h ? @@:323___PPT103.<+o%D2' = @B Di2' = @BA?%,( < +O%,( < +D-' =%(D' =%(D}' =A@BB1BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*#%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*#D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*#D' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*#D' =-g6B fade*<3<*#D-' =%(D' =%(D}' =A@BB1BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*#J%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*#JD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*#JD' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*#JD' =-g6B fade*<3<*#JD-' =%(D' =%(D}' =A@BB1BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*J^%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*J^D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*J^D' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*J^D' =-g6B fade*<3<*J^D-' =%(D' =%(D}' =A@BB1BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*^{%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*^{D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*^{D' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*^{D' =-g6B fade*<3<*^{D-' =%(D' =%(D}' =A@BB1BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*{%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*{D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*{D' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*{D' =-g6B fade*<3<*{D-' =%(D' =%(D}' =A@BB1BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*D' =-g6B fade*<3<*D-' =%(D' =%(D}' =A@BB1BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*D' =-g6B fade*<3<*D-' =%(D' =%(D}' =A@BB1BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*D' =-g6B fade*<3<*+8+0+C +}  $(  r  S Yp`   r  S 䭟Yp   H  0޽h ? @@___PPT10i.:x+D=' = @B +C  )! (  r  S RYp`  R   S RY<$ 0 R a   fRxaxa 1?"6@`NNN?N  !POSITIONAL ACCURACY HANDBOOK 1999&" nK2" ! 8H  0޽h ? @@  ___PPT10 .|+=D6 ' = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*e%(D' =-6B'blinds(horizontal)*<3<*eD' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*e%(D' =-6B'blinds(horizontal)*<3<*eD' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =-6B'blinds(horizontal)*<3<*,+8+0+R +   f(  r  S PRYp`  R   S R Ypv<$ 0 R "p`PpH  0޽h ? @@  ___PPT10f .}p+qD ' = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(DG' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*A%(D' =+v4 ,0B*O3> B<*AD' =%(D' =%(DG' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Ah%(D' =+v4 ,0B*O3> B<*AhD' =%(D' =%(DG' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =+v4 ,0B*O3> B<*hD' =%(D' =%(DG' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+v4 ,0B*O3> B<*+8+0+R +#   @(  x  c $HRYp`  R   c $R Ypv<$  0 R "p`Pp @  `xaxa 1?"6@ NNN?N  H  0޽h ? @@___PPT10.}p++dD' = @B DJ' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*I%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*ID' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*ID{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*I%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*ID' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*ID{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*+8+0+R +  0\F(  \x \ c $4RYp`  R  \ c $R Ypv R "p`PpH \ 0޽h ? @@___PPT10i.}p+D=' = @B +  |F(  |x | c $lRYp`  R  | c $Yp R "p`PpH | 0޽h ? @@___PPT10i.}p+D=' = @B +(    [ (  r  S dYp`    0  6xaxaA     ? A@  A1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab J    c $ZY <$ 0  a   fxaxa 1?"6@`NNN?N C !POSITIONAL ACCURACY HANDBOOK 1999&" nK2" ! 8H  0޽h ? @@z___PPT10Z.P+ D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*>%(D' =-o6Bdissolve*<3<*>D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*>]%(D' =-o6Bdissolve*<3<*>]D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*]h%(D' =-o6Bdissolve*<3<*]hD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*hx%(D' =-o6Bdissolve*<3<*hxD ' =%(D ' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-o6Bdissolve*<3<*xD@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*+8+0+ +  @`F(  `x ` c $Yp`    ` c $ Ypv  "p`PpH ` 0޽h ? @@___PPT10i.}p+D=' = @B +k)  )! (  r  S (Yp`     S ) Ypv<$  0  a   f0xaxa 1?"6@`NNN?N C !POSITIONAL ACCURACY HANDBOOK 1999&" nK2" ! 8H  0޽h ? @@%%___PPT10%. i++B#style.visibility<*%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D+' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*!%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*!D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*!D' =%(D+' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*!7%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*!7D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*!7D' =%(D+' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*7a%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*7aD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*7aD' =%(D+' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*a{%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*a{D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*a{D' =%(D+' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*{%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*{D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*{D' =%(D+' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D+' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*+8+0+ +m  | X(  Xx X c $xCYp`    X c $I Ypv  "p`Pp X@  `xaxa 1?"6@ NNN?N  H X 0޽h ? @@___PPT10i.}p+D=' = @B +#!     f (  r  S SYp`    0 C x0e0eA ?5% ?0 H $D  0  0 C x0e0eA ?5% ?"` Pt   a   fXoTxaxa 1?"6@`NNN?N C !POSITIONAL ACCURACY HANDBOOK 1999&" nK2" ! 8z   0A ? ?"`  w   fWxaxa 1?"6@ NNN?N+ pp ,$ 0 oSi:& nK2 8  6A ? ?"` 8 $D  0   f@ixaxa 1?"6@ NNN?N 0],$  0 NErrorx independiente de Errory Errores con distribucin Normal No hay outliersZO nK2  0N 8r  # lxaxa 1?"6@`NNN?N`,$D  0  S xaxa2W>d?f P 6Es un test paramtrico!Impact"6@ NNN?N @  ,$D 0H  0޽h ? @@___PPT10.-_ +HD1' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bwipe(up)*<3<*D' =%(D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bwipe(up)*<3<*Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*+p+0+ ++0+ +  UM`  (  x  c $k Yp`     0 S ~0e0eA ?5% ?"` )   a   fxaxa 1?"6@`NNN?N C !POSITIONAL ACCURACY HANDBOOK 1999&" nK2" ! 8w   fxaxa 1?"6@ NNN?N+ pp ,$ 0 oSi:& nK2 8  6A ? ?"`; 8 $D 0    f$xaxa 1?"6@ NNN?N `i ,$  0 /Errores con distribucin Normal No hay outliers&0 nK20/ 8r   # lxaxa 1?"6@`NNN?N `` ,$D  0H  0޽h ? @@___PPT10.-_ +!D[' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(down)*<3<* D' =%(D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bwipe(up)*<3<* Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*+p+0+ ++0+  + +   ?(   r   S Y`      S  Ypv<$ 0     0Ԫ #" `P P ) Arthur J. Lembo, Jr. Cornell University *0*0     S 4xaxaHW>d?f P 6Algunos sern ms graves que otrosImpact"6@ NNN?N P 2,$D  0H   0޽h ? @@&%___PPT10%.+S\Dv%' = @B D1%' = @BA?%,( < +O%,( < +D' =%(D' =%(DG' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+v4 ,0B*O3> B<* D' =%(D' =%(DG' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 9%(D' =+v4 ,0B*O3> B<* 9D' =%(D' =%(DG' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 9S%(D' =+v4 ,0B*O3> B<* 9SD' =%(D' =%(DG' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* Sw%(D' =+v4 ,0B*O3> B<* SwD' =%(D' =%(DG' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* w%(D' =+v4 ,0B*O3> B<* wD' =%(D' =%(DG' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+v4 ,0B*O3> B<* D' =%(D' =%(DG' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+v4 ,0B*O3> B<* D' =%(D' =%(DG' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+v4 ,0B*O3> B<* Dp ' =%(D ' =%(D ' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(DO' =+4 8?HCBBCBB*k3>'Bstyle.rotation<* %())?DY' =+4 8?dCB#ppt_wBCB#ppt_w*.05B*Y3>B ppt_w<* %())?DY' =+4 8?dCB#ppt_w*.05BCB#ppt_wB*Y3>B ppt_w<* %()?)D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<* DW' =+4 8?bCB#ppt_x+.4BCB#ppt_xB*Y3>B ppt_x<* %())?D]' =+4 8?hCB#ppt_y-.2BCB#ppt_y+.1B*Y3>B ppt_y<* %())?DW' =+4 8?bCB#ppt_y+.1BCB#ppt_yB*Y3>B ppt_y<* %()?)D' =-g6B fade*<3<* %())?+8+0+  +P  :&2&Bc %(  r  S XYp`     S T Ypv<$ 0  #l   b g,$D  0T @[ 0#   1 H?"`@[ oDatos40 2 H ?"`@[ @ 0 aT Z  # 0  H<?Z  qTerreno40x  H ?Z T Z @ '#   ( H`?Z @ aA20 x ) H ?Z @T  \@ *#   + H? \@ aB20 x , H ? \@T \ @ -#   . H?\ @ aC20 x / H ?\ @JT [@[` 3#  q f 4 6?[@[`x 5 H ?[@[`T [@Z` 6#  q  7 H?[@Z` aA20 x 8 H ?[@Z`T Z@` 9#  q  : H ?Z@` R10"0 x ; H ?Z@`T @\` <#  q  = H?@\` Q2"0 x > H ?@\`T \@` ?#  q  @ H?\@` Q3"0 x A H ?\@`JT [`[ B# q 1 f C 6?[`[x D H ?[`[T [`Z E# q 1  F H?[`Z aB20 x G H ?[`ZT Z` H# q 1  I H?Z` Q0"0 x J H ?Z`T `\ K# q 1  L H?`\ R20"0 x M H ?`\T \` N# q 1  O H?\` Q0"0 x P H ?\`JT [[ Q# 1 f R 6?[[x S H ?[[T [Z T# 1  U H ?[Z aC20 x V H ?[ZT Z W# 1  X H ?Z Q4"0 x Y H ?ZT \ Z# 1  [ H?\ Q1"0 x \ H ?\T \ ]# 1  ^ H?\ R10"0 x _ H ?\V c # xaxa8W?Exactitud global=traza(A)/NArial Black"6@`NNN?NP,$D  0H  0޽h ? @@**"*___PPT10*.I!/+jD)' = @B DY)' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 7%(D' =-o6Bdissolve*<3<* 7D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*7R%(D' =-o6Bdissolve*<3<*7RD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Ro%(D' =-o6Bdissolve*<3<*RoD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*o%(D' =-o6Bdissolve*<3<*oD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*Dp ' =%(D ' =%(D ' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*b%(DO' =+4 8?HCBBCBB*k3>'Bstyle.rotation<*b%())?DY' =+4 8?dCB#ppt_wBCB#ppt_w*.05B*Y3>B ppt_w<*b%())?DY' =+4 8?dCB#ppt_w*.05BCB#ppt_wB*Y3>B ppt_w<*b%()?)D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*bDW' =+4 8?bCB#ppt_x+.4BCB#ppt_xB*Y3>B ppt_x<*b%())?D]' =+4 8?hCB#ppt_y-.2BCB#ppt_y+.1B*Y3>B ppt_y<*b%())?DW' =+4 8?bCB#ppt_y+.1BCB#ppt_yB*Y3>B ppt_y<*b%()?)D' =-g6B fade*<3<*b%())?DP' =%(D' =%(D' =4@BB'BB%()?D' =1:Bvisible*o3>+B#style.visibility<*c%(DK' =+4 8?CB#ppt_h/20BCB#ppt_h/20BCB#ppt_hB*Y3>B ppt_h<*cDK' =+4 8?CB#ppt_w+.3BCB#ppt_w+.3BCB#ppt_wB*Y3>B ppt_w<*cDE' =+ 4 8?CB#ppt_x-.3BCB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*cD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*c+8+0+ +B   P(  r  S &Yp`     S ' Ypv<$ 0  H  0޽h ? @@*"___PPT10.+GD' = @B DY' = @BA?%,( < +O%,( < +D`' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =-6B'blinds(horizontal)*<3<*\D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*\o%(D' =-6B'blinds(horizontal)*<3<*\oD' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*o%(D' =-6B'blinds(horizontal)*<3<*oD' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*+8+0+ +/  $$0ABt$(  r  S 2Yp`     N4  p)p? P<$ 0  "F     0;T @[ #    Hd9?"`@[ oDatos40  H ?"`@[ N 0   T Z   # 0   H=?Z  qTerreno40x   H ?Z T Z @  #    HB?Z @ aA20 x  H ?Z @T  \@ #    HG? \@ aB20 x  H ? \@T \ @ #    HL?\ @ aC20 x  H ?\ @JT [@[` #  q f  6?[@[`x  H ?[@[`T [@Z` #  q   HpR?[@Z` aA20 x  H ?[@Z`T Z@` #  q   HV?Z@` R10"0 x  H ?Z@`T @\` #  q    HZ?@\` Q2"0 x ! H ?@\`T \@` "#  q  # H_?\@` Q3"0 x $ H ?\@`JT [`[ %# q 1 f & 6?[`[x ' H ?[`[T [`Z (# q 1  ) H$d?[`Z aB20 x * H ?[`ZT Z` +# q 1  , Hh?Z` Q0"0 x - H ?Z`T `\ .# q 1  / H m?`\ R20"0 x 0 H ?`\T \` 1# q 1  2 HTq?\` Q0"0 x 3 H ?\`JT [[ 4# 1 f 5 6?[[x 6 H ?[[T [Z 7# 1  8 H`v?[Z aC20 x 9 H ?[ZT Z :# 1  ; H({?Z Q4"0 x < H ?ZT \ =# 1  > H\?\ Q1"0 x ? H ?\T \ @# 1  A H?\ R10"0 x B H ?\H  0޽h ? @@z r ___PPT10R ..C+FD ' = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*A%(D' =-o6Bdissolve*<3<*AD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*A%(D' =-o6Bdissolve*<3<*AD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*+8+0+ +  @ (   r   S |Yp`     0  0e0eA) ?5%?7   H   0޽h ? @@___PPT10i.˳+D=' = @B +?#  `(P(  (r ( S (Yp`    ( S $Yp<$  0  H ( 0޽h ? @@'!!___PPT10 .P,:++dD ' = @B DV ' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(@%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*(@D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*(@D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(@`%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*(@`D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*(@`D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(`%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*(`D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*(`D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*(D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*(D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*(D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*(D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(/%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*(/D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*(/D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(/A%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*(/AD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*(/A+8+0+( +  p,_(  ,r , S Yp`    , c $İ <$ 0  "P@08X ,0  0e0eA+ ?5%?d    ,  fxxaxa 1?"6@ NNN?N   ,$ 0 ?qA=15*14/50=4.20 qB=20*23/50=9.20 qC=15*13/50=3.90 q=Total=17.3t@ nK2          ? H , 0޽h ? @@  ___PPT10 .+])D ' = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =-o6Bdissolve*<3<*,D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,W%(D' =-o6Bdissolve*<3<*,WD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,Wr%(D' =-o6Bdissolve*<3<*,WrD' =%(D' =%(DL' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =-{6Bslide(fromTop)*<3<*,+p+0+, ++0+, +r*  &4(  4x 4 c $,Yp`    4 s *  <$ 0  "P@08X 40  0e0eA( ?5%?d    4  f0xaxa 1?"6@ NNN?N  ,$ 0  Kappa=(40-17.3)/(50-40) =0.227&! nK2!   4 c xaxa$WG7>d?f P 6Bastante malo! Impact"6@ NNN?N 0 l,$D 0H 4 0޽h ? @@##___PPT10#.+yD0#' = @B D"' = @BA?%,( < +O%,( < +D} ' =%(D% ' =%(D ' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(DO' =+4 8?HCBBCBB*k3>'Bstyle.rotation<*4%())?DY' =+4 8?dCB#ppt_wBCB#ppt_w*.05B*Y3>B ppt_w<*4%())?DY' =+4 8?dCB#ppt_w*.05BCB#ppt_wB*Y3>B ppt_w<*4%()?)D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*4DW' =+4 8?bCB#ppt_x+.4BCB#ppt_xB*Y3>B ppt_x<*4%())?D]' =+4 8?hCB#ppt_y-.2BCB#ppt_y+.1B*Y3>B ppt_y<*4%())?DW' =+4 8?bCB#ppt_y+.1BCB#ppt_yB*Y3>B ppt_y<*4%()?)D' =-g6B fade*<3<*4%())?D} ' =%(D% ' =%(D ' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4.%(DO' =+4 8?HCBBCBB*k3>'Bstyle.rotation<*4.%())?DY' =+4 8?dCB#ppt_wBCB#ppt_w*.05B*Y3>B ppt_w<*4.%())?DY' =+4 8?dCB#ppt_w*.05BCB#ppt_wB*Y3>B ppt_w<*4.%()?)D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*4.DW' =+4 8?bCB#ppt_x+.4BCB#ppt_xB*Y3>B ppt_x<*4.%())?D]' =+4 8?hCB#ppt_y-.2BCB#ppt_y+.1B*Y3>B ppt_y<*4.%())?DW' =+4 8?bCB#ppt_y+.1BCB#ppt_yB*Y3>B ppt_y<*4.%()?)D' =-g6B fade*<3<*4.%())?D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-o6Bdissolve*<3<*4D ' =%(D' =%(Dp' =4@BB1BB%()?D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*4D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*4D' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*4D' =-g6B fade*<3<*4+p+0+4 ++0+4 +  8P(  8r 8 S Yp`    8 S  Ypv<$ 0  H 8 0޽h ? @@___PPT10c. tT+o D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DG' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8J%(D' =+v4 ,0B*O3> B<*8JD' =%(D' =%(DG' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8JZ%(D' =+v4 ,0B*O3> B<*8JZD' =%(D' =%(DG' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8Zs%(D' =+v4 ,0B*O3> B<*8ZsD' =%(D' =%(DG' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8s%(D' =+v4 ,0B*O3> B<*8sD' =%(D' =%(DG' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =+v4 ,0B*O3> B<*8D' =%(D' =%(DG' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =+v4 ,0B*O3> B<*8D' =%(D' =%(DG' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =+v4 ,0B*O3> B<*8+8+0+8 +  P(  r  S 8CYp`     S 4C Ypv<$ 0 C H  0޽h ? @@xp___PPT10P.!+LFD' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"%(D' =-6B%slide(fromBottom)*<3<*"D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"I%(D' =-6B%slide(fromBottom)*<3<*"ID' =%(D^' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Ij%(D' =-6B%slide(fromBottom)*<3<*IjDR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*jx%(D' =-6B%slide(fromBottom)*<3<*jxDR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-6B%slide(fromBottom)*<3<*xD' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*+8+0+C +E  <b(  <r < S RYp`  R r < S R Yp v R J <  xaxa2W?Componentes ms modernasArial Black"6@ NNN?N  ,$D 0F <  xaxa.W?Sin definir totalmenteArial Black"6@ NNN?N  ,$D 0P <  xaxa8W?Falta unificar nomenclaturaArial Black"6@ NNN?NP ^,$D 0> < # xaxa W?Faltan mtricasArial Black"6@`NNN?N@,$D 0H < 0޽h ? @@>>___PPT10>. "+=Db>' = @B D>' = @BA?%,( < +O%,( < +Ds' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' D=-s6Bwipe(down)*<3<*<%(D' =eB]0,0; 0.14,0.36; 0.43,0.73; 0.71,0.91; 1.0,1.0+4 8?fCB#ppt_x-0.25BCB#ppt_xB*Y3>B ppt_x<*<%(D' =mBe0.0,0.0; 0.25,0.07; 0.50,0.2; 0.75,0.467; 1.0,1.0+4 8?lCB?B'#ppt_y-sin(pi*$)/3CB?B*Y3>B ppt_y<*<%(D' =B0, 0; 0.125,0.2665; 0.25,0.4; 0.375,0.465; 0.5,0.5; 0.625,0.535; 0.75,0.6; 0.875,0.7335; 1,1+4 8?lCBB'#ppt_y-sin(pi*$)/9CB?B*Y3>B ppt_y<*<%(D' L=B0, 0; 0.125,0.2665; 0.25,0.4; 0.375,0.465; 0.5,0.5; 0.625,0.535; 0.75,0.6; 0.875,0.7335; 1,1+4 8?nCBB)#ppt_y-sin(pi*$)/27CB?B*Y3>B ppt_y<*<%(,D' =B0, 0; 0.125,0.2665; 0.25,0.4; 0.375,0.465; 0.5,0.5; 0.625,0.535; 0.75,0.6; 0.875,0.7335; 1,1+4 8?nCBB)#ppt_y-sin(pi*$)/81CB?B*Y3>B ppt_y<*<%(xD' =0l9 BBBpB*<3<*<%(D' =0l9 BBBB*<3<*<%())?D' =0l9 BBBB*<3<*<%( D' =0l9 BBBB*<3<*<%(:))?D' =0l9 BBBB*<3<*<%(jD' =0l9 BBBB*<3<*<%())?D' =0l9 BBBB*<3<*<%(D' =0l9 BBBB*<3<*<%(*))?Ds' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' D=-s6Bwipe(down)*<3<*<%(D' =eB]0,0; 0.14,0.36; 0.43,0.73; 0.71,0.91; 1.0,1.0+4 8?fCB#ppt_x-0.25BCB#ppt_xB*Y3>B ppt_x<*<%(D' =mBe0.0,0.0; 0.25,0.07; 0.50,0.2; 0.75,0.467; 1.0,1.0+4 8?lCB?B'#ppt_y-sin(pi*$)/3CB?B*Y3>B ppt_y<*<%(D' =B0, 0; 0.125,0.2665; 0.25,0.4; 0.375,0.465; 0.5,0.5; 0.625,0.535; 0.75,0.6; 0.875,0.7335; 1,1+4 8?lCBB'#ppt_y-sin(pi*$)/9CB?B*Y3>B ppt_y<*<%(D' L=B0, 0; 0.125,0.2665; 0.25,0.4; 0.375,0.465; 0.5,0.5; 0.625,0.535; 0.75,0.6; 0.875,0.7335; 1,1+4 8?nCBB)#ppt_y-sin(pi*$)/27CB?B*Y3>B ppt_y<*<%(,D' =B0, 0; 0.125,0.2665; 0.25,0.4; 0.375,0.465; 0.5,0.5; 0.625,0.535; 0.75,0.6; 0.875,0.7335; 1,1+4 8?nCBB)#ppt_y-sin(pi*$)/81CB?B*Y3>B ppt_y<*<%(xD' =0l9 BBBpB*<3<*<%(D' =0l9 BBBB*<3<*<%())?D' =0l9 BBBB*<3<*<%( D' =0l9 BBBB*<3<*<%(:))?D' =0l9 BBBB*<3<*<%(jD' =0l9 BBBB*<3<*<%())?D' =0l9 BBBB*<3<*<%(D' =0l9 BBBB*<3<*<%(*))?Ds' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' D=-s6Bwipe(down)*<3<*<%(D' =eB]0,0; 0.14,0.36; 0.43,0.73; 0.71,0.91; 1.0,1.0+4 8?fCB#ppt_x-0.25BCB#ppt_xB*Y3>B ppt_x<*<%(D' =mBe0.0,0.0; 0.25,0.07; 0.50,0.2; 0.75,0.467; 1.0,1.0+4 8?lCB?B'#ppt_y-sin(pi*$)/3CB?B*Y3>B ppt_y<*<%(D' =B0, 0; 0.125,0.2665; 0.25,0.4; 0.375,0.465; 0.5,0.5; 0.625,0.535; 0.75,0.6; 0.875,0.7335; 1,1+4 8?lCBB'#ppt_y-sin(pi*$)/9CB?B*Y3>B ppt_y<*<%(D' L=B0, 0; 0.125,0.2665; 0.25,0.4; 0.375,0.465; 0.5,0.5; 0.625,0.535; 0.75,0.6; 0.875,0.7335; 1,1+4 8?nCBB)#ppt_y-sin(pi*$)/27CB?B*Y3>B ppt_y<*<%(,D' =B0, 0; 0.125,0.2665; 0.25,0.4; 0.375,0.465; 0.5,0.5; 0.625,0.535; 0.75,0.6; 0.875,0.7335; 1,1+4 8?nCBB)#ppt_y-sin(pi*$)/81CB?B*Y3>B ppt_y<*<%(xD' =0l9 BBBpB*<3<*<%(D' =0l9 BBBB*<3<*<%())?D' =0l9 BBBB*<3<*<%( D' =0l9 BBBB*<3<*<%(:))?D' =0l9 BBBB*<3<*<%(jD' =0l9 BBBB*<3<*<%())?D' =0l9 BBBB*<3<*<%(D' =0l9 BBBB*<3<*<%(*))?D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-o6Bdissolve*<3<*<+   @6(  @r @ S RYp`  R x @ c $R Y v R  @ # z0e0eA*5% NEWARK p  RB @ # xaxa$W?Cmo lo medira?Arial Black"6@`NNN?N `,$D 0H @ 0޽h ? @@___PPT10. +EgD^' = @B D' = @BA?%,( < +O%,( < +DP' =%(D' =%(D' =4@BB'BB%()?D' =1:Bvisible*o3>+B#style.visibility<*@%(DK' =+4 8?CB#ppt_h/20BCB#ppt_h/20BCB#ppt_hB*Y3>B ppt_h<*@DK' =+4 8?CB#ppt_w+.3BCB#ppt_w+.3BCB#ppt_wB*Y3>B ppt_w<*@DE' =+ 4 8?CB#ppt_x-.3BCB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*@D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*@+m  |P(  Px P c $Yp`    P c $< Ypv  "p`Pp P@  `xaxa 1?"6@ NNN?N  H P 0޽h ? @@___PPT10i.}p+D=' = @B +  ?7P (  r  S ̰Yp`     S h! Ypv<$ 0  "p`Ppa   f+xaxa 1?"6@`NNN?N C !POSITIONAL ACCURACY HANDBOOK 1999&" nK2" ! 8H  0޽h ? @@jb___PPT10B./+n_|D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*+%(D' =-o6Bdissolve*<3<*+D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*+k%(D' =-o6Bdissolve*<3<*+kD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*k%(D' =-o6Bdissolve*<3<*kD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*O%(D' =-o6Bdissolve*<3<*O+8+0+  +r  0(  x  c $8Yp`   x  c $9 Ypv  H  0޽h ? @@zr___PPT10R.g0Μ+D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*:%(D' =-s6Bwipe(down)*<3<*:D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*:]%(D' =-s6Bwipe(down)*<3<*:]D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*]%(D' =-s6Bwipe(down)*<3<*]D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*+8+0+ +l-  4,(  x  c $AYp`   x  c $BY    S &xaxa:W>d?f P 6Permanezca en este canal!Impact"6@ NNN?NP vH  0޽h ? @@))___PPT10).j+DT)' = @B D)' = @BA?%,( < +O%,( < +D' =%(Do' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*@D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*@D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@]%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*@]D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*@]D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*]z%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*]zD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*]zD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*z%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*zD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*zD' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*+8+0+ +m  |Pd(  dx d c $ZYp`    d c $Xa Ypv  "p`Pp d@  `xaxa 1?"6@ NNN?N  H d 0޽h ? @@___PPT10i.}p+D=' = @B +  )! (  r  S (kYp`     S $l Yv<$  0  a   flmxaxa 1?"6@`NNN?N C !POSITIONAL ACCURACY HANDBOOK 1999&" nK2" ! 8H  0޽h ? @@ z ___PPT10Z .3@[+|9D ' = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*M%(D' =-s6Bwipe(down)*<3<*MD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*M%(D' =-s6Bwipe(down)*<3<*MD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*+8+0+ +  ` h0(  hr h S xYp`    h S t  @ <$  0   h  fxaxa ?"6@`NNN?Np pi,$D 0 ^Atencin: Lo que de all resulte complementa, pero no sustituye a lo requerido por el estndar,_( nK_ ^ H h 0޽h ? @@"___PPT10.>@7+^*)D^' = @B D' = @BA?%,( < +O%,( < +D' =%(D+' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*hD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*hD' =%(D+' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*hD%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*hDD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*hDD' =%(D+' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*hDf%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*hDfD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*hDfD' =%(D+' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*hf%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*hfD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*hfD$' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*hD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*hD' =-g6B fade*<3<*h+p+0+h ++0+h +   (  e   fؙxaxa 1?"6@ NNN?N0z  Breve introduccin al Bootstrap, ( nK2 6 H  0޽h ? @@___PPT10i.;'V+D=' = @B +   p lU(  l~ l s *(Yp`    l s *D Y0v<$ 0   l 0 "`  wFuente: Lucila Ohno-Machado$ H l 0޽h ? ̙33j b ___PPT10B + D ' = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*lB%(D' =-o6Bdissolve*<3<*lBD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*lB%(D' =-o6Bdissolve*<3<*lBD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*l%(D' =-o6Bdissolve*<3<*l+8+0+l +l   ph(  p~ p s *HYp`    p s *DY0<$ 0  H p 0޽h ? ̙33<4___PPT10+4PD' = @B D{' = @BA?%,( < +O%,( < +D' =%(D' =%(D:' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p9%(D' =-i6B wedge*<3<*p9D' =%(D' =%(D:' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p9b%(D' =-i6B wedge*<3<*p9bD' =%(D' =%(D:' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*pb%(D' =-i6B wedge*<3<*pbD' =%(D' =%(D:' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p %(D' =-i6B wedge*<3<*p D' =%(D' =%(D:' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p e%(D' =-i6B wedge*<3<*p e+8+0+p +   t<(  t~ t s *Yp`   ~ t s * Ypv  H t 0޽h ? ̙33y___PPT10Y+D=' = @B +  ""xF(  xz pp  x# #"&pp x <?p p  Y3  @` x <8?@ p p  Z41  @` x <h?p @ p  Z44  @` x <?p p  Y4  @` x <?p p  Y5  @` x <?@ p p  Z35  @`  x < ?p @ p  Z40  @`  x <?p p  Y3  @`  x <?pp  Z-3  @`  x <T$?@ pp  Z17  @`  x <l,?p@ p  Z14  @` x <84?pp  Y2  @` x <=?pp Y6  @` x <E?@ pp Z18  @` x <M?p@ p Z24  @` x <0V?pp Y1  @` x <P?pp _Differ.  @` x <f?@ pp eMujer @` x <o?p@ p fHombre @` x < x?pp iObserv. @`ZB x s *1 ?ppZB x s *1 ?ppZB x s *1 ?ppZB x s *1 ?p p ZB x s *1 ?p p `B x 0o ?p p `B x 0o ?pp ZB x s *1 ?pp ZB x s *1 ?@ p@ p ZB  x s *1 ?pp `B !x 0o ?pp `B "x 0o ?ppH x 0޽h ? ̙33y___PPT10Y+D=' = @B +    |(  |~ | s *tYp`    | s * 7  "P@08X` | c $A6 ??C@@  | c $A ??L  8 $D 0 | C xpxaxa 1?"6@ NNN?N ? ,$  0 0Problema: no conocemos sD0 nKZ    | Z\xaxa1 ?  7 ,$ 0 <Si Y fuese normal, el Intervalo de Confianza CI al 95% seraZ"P@08XH | 0޽h ? ̙33  ___PPT10l +(D ' = @B D ' = @BA?%,( < +O%,( < +DO' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =-6B%slide(fromBottom)*<3<*|DE' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =-6B%slide(fromBottom)*<3<*|D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*|D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*|+p+0+| ++0+| +   t(  ~  s *8Yp`   ~  s * Y`  `  c $A ??`0  `  c $A ??   `  c $A ??  H  0޽h ? ̙33y___PPT10Y+D=' = @B +m   $(  ~  s *Yp`   ~  s *p Yp   `  c $A ??Pp $ x  S xaxa&W3fv @?f P 6GIGANTESCO!!! Impact"6@ NNN?N p./H  0޽h ? ̙33y___PPT10Y+D=' = @B +   <(  ~  s *Y`   ~  s *T Wv  H  0޽h ? ̙33y___PPT10Y+D=' = @B +U  BB []"B(  ~  s *Yp`   9 | V #":. |  <?6| \3.00  @`  <?6| Y3  @`  <L? 6| Y3  @`  <?`6 | Y3  @`  <?86`| Y3  @`   <?68| [256  @`   <$ ? 6 [3.5  @`   <? 6 Y5  @`   <? 6 Y3  @`   <$?` 6 Y3  @`  <.?8 `6 Z-3  @`  <P/? 86 [255  @`  <7?   > @`  <F?   > @`  <H?   > @`  <W?`  > @`  <_?8 `  > @`  <th? 8  Z&   @`  <p?d   \1.25  @`  <x?d   Y6  @`  <8k? d   Z-3  @`  <̈?`d  Y5  @`  <?8d `  Z-3  @`  <X?d 8  [101  @`  <p? d  \2.75  @`  <<? d  Y3  @`  <?  d  Y6  @`  <Ȼ?` d  Y5  @`   <?8 `d  Z-3  @` ! <? 8d  [100  @` " <l?  > @` # <?  > @` $ <?   > @` % <?`   > @` & <P?8`  > @` ' <|?8  Z..  @` ( <d? \5.75  @` ) <8? Y5  @` * <?  Y6  @` + <?`  Y6  @` , <(?8` Y6  @` - <l0?8 Y3  @` . <9?L \3.75  @` / <A?L Z-3  @` 0 <J? L Y6  @` 1 <Q?`L  Y6  @` 2 <([?8L` Y6  @` 3 <hc?L8 Y2  @` 4 <k?L \6.00  @` 5 <Ls?L Y6  @` 6 <|? L Y6  @` 7 <؄?` L Y6  @` 8 <?8`L Y6  @` 9 <?8L Y1  @` : <? ] *  @` ; <? mY4*&  @` < <?  mY3*&  @` = <?`  mY2*&  @` > <0?8` mY1*&  @` ? <?8 iMuestra @`ZB @ s *1 ?ZB A s *1 ?LLZB B s *1 ?ZB C s *1 ?ZB D s *1 ?  ZB E s *1 ?d d ZB F s *1 ?  ZB G s *1 ?  ZB H s *1 ?66`B I 0o ?||`B J 0o ?|ZB K s *1 ?88|ZB L s *1 ?``|ZB M s *1 ?  |ZB N s *1 ?|ZB O s *1 ?|`B P 0o ?|ZB Q s *1 ?8``B R 0o ?8`B S 0o ?`` T c $A ??0   W  fLxaxaGH8J1?"6@`NNN?Np0@,$D 0 Slo hay 256 posibilidades(( nK  l  @ @ ]@ @,$D  0w Y S ~,xaxaGx<HSI*VJK*VMU ?"6@`NNN?N @ @  Otro caso extremo,( nK  2 Z  fxaxa  ?"6@`NNN?N l P@ \P@,$D 0r X S ~`xaxaGx<HSI*VJK*VMU ?"6@`NNN?N @ ~ Caso extremo, ( nK    2 [  fxaxa  ?"6@`NNN?NP@H  0޽h ??0WXY ̙33___PPT10+SD ' = @B D' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =%(D' =%(D1' =4@BB BB%(D' =-o6Bdissolve*<3<*\D' =1:Bhidden*o3>+B#style.visibility<*\%(D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*]%(D' =-s6Bwipe(down)*<3<*]D' =%(D' =%(D1' =4@BB BB%(D' =-o6Bdissolve*<3<*]D' =1:Bhidden*o3>+B#style.visibility<*]%(D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*W%(D' =-o6Bplus(in)*<3<*WD' =%(D' =%(DV' =A@BBB B0B%(D' =-6B+checkerboard(across)*<3<*WD' =1:Bhidden*o3>+B#style.visibility<*W%(+p+0+W ++0+W +H  .&(  ~  s *, Yp`   ~  s *  Y`v   `  c $A ??o}` `  c $A ??Z    S xaxa$W>d?f P 6Igual que antes!Impact"6@ NNN?N`  ,$D 0H  0޽h ? ̙33  ___PPT10 +|3D~ ' = @B D9 ' = @BA?%,( < +O%,( < +Dp ' =%(D ' =%(D ' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(DO' =+4 8?HCBBCBB*k3>'Bstyle.rotation<*%())?DY' =+4 8?dCB#ppt_wBCB#ppt_w*.05B*Y3>B ppt_w<*%())?DY' =+4 8?dCB#ppt_w*.05BCB#ppt_wB*Y3>B ppt_w<*%()?)D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*DW' =+4 8?bCB#ppt_x+.4BCB#ppt_xB*Y3>B ppt_x<*%())?D]' =+4 8?hCB#ppt_y-.2BCB#ppt_y+.1B*Y3>B ppt_y<*%())?DW' =+4 8?bCB#ppt_y+.1BCB#ppt_yB*Y3>B ppt_y<*%()?)D' =-g6B fade*<3<*%())?+  h(  ~  s * Yp`     s *  Yv<$ 0   H  0޽h ? ̙33VN___PPT10.+o%D' = @B D' = @BA?%,( < +O%,( < +D-' =%(D' =%(D}' =A@BB1BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*D' =-g6B fade*<3<*D-' =%(D' =%(D}' =A@BB1BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*;%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*;D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*;D' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*;D' =-g6B fade*<3<*;D-' =%(D' =%(D}' =A@BB1BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*;o%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*;oD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*;oD' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*;oD' =-g6B fade*<3<*;oD-' =%(D' =%(D}' =A@BB1BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*o%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*oD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*oD' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*oD' =-g6B fade*<3<*o+8+0+  +   (  ~  s *  Yp       f, xaxa ?"6@`NNN?N p,$D 0 `En la prctica (a diferencia del ejemplo anterior), no todas las NN remuestras son seleccionadasZa nK7      H  0޽h ? ̙33zr___PPT10R+MC D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*+8+0+  +  x0(  ~  s *5 Yp`     s *;  Ypv   "p`Pp   fH xaxaGHr1?"6@`NNN?N @,$D  0 `Lase como  el criterio aplicado a la poblacin (1( nK1 0   Z V xaxa1 ? )@,$  0 2. Use esta muestra como si fuese la poblacin (pero con reemplazo) Criterio(muestra) re-muestra1 re-muestra2 etc& DP5 +~< p`PpH  0޽h ? ̙33  ___PPT10 +DD ' = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D' =%(D' =%(DB' =A@BBBB0B%(D' =-s6Bwipe(down)*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*++0+  ++0+  ++0+  +  @<(  ~  s *0b Yp`   ~  s *,d  Ypv   H  0޽h ? ̙33y___PPT10Y+D=' = @B +   #(  r  S i Yp`   r  S k  Yp      # lu xaxa1?"6@`NNN?N9` Ahttp://www.itl.nist.gov/div898/handbook/eda/section3/bootplot.htm&B nKBA 8H  0޽h ? @@___PPT10i.ޙp.r+D=' = @B +  U(  r  S } Yp`   x  c $} Y    0 3 r0e0eA' ?5% ?C P   w  C x xaxa 1?"6@`NNN?Nj Ahttp://www.itl.nist.gov/div898/handbook/eda/section4/eda4222.htm &B nKB 0 c 0e0eA! ?5% ?"`` R   H  0޽h ? @@___PPT10i.@{+D=' = @B +n1  (  x  c $ Yp`    $  C 0e0eA 5%$runseqrun sequence plot"` g  <$D 0    # 0e0eA"5%lagplotlag plot a # <$D 0  0  # 0e0eA#5%Fhistnormhistogram with overlaid normal PDF{ g v<$D 0    # 0e0eA$5%0normprplnormal probability plot{ a #v<$D 0  @   xaxa.W?No luce como normal...Arial Black"6@ NNN?NP~8,$D 0H  0޽h ? @@&**___PPT10).Ӕ+AϰD)' = @B D)' = @BA?%,( < +O%,( < +DU' =%(D' =%(D' =4@BB3BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*)?D' =0l9 BB A AHCC*<3<*)?D' =0l9 BBHCCBB*<3<*%()?D' =1:B (0.5)*Y3>B ppt_x<*D ' =+4 . B (0.5)0B(#ppt_x)*Y3>B ppt_x<*%()?D' =1:B(#ppt_y+0.4)*Y3>B ppt_y<*D' =+4 . B(#ppt_y+0.4)0B(#ppt_y)*Y3>B ppt_y<*%()?DU' =%(D' =%(D' =4@BB3BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*)?D' =0l9 BB A AHCC*<3<*)?D' =0l9 BBHCCBB*<3<*%()?D' =1:B (0.5)*Y3>B ppt_x<*D ' =+4 . B (0.5)0B(#ppt_x)*Y3>B ppt_x<*%()?D' =1:B(#ppt_y+0.4)*Y3>B ppt_y<*D' =+4 . B(#ppt_y+0.4)0B(#ppt_y)*Y3>B ppt_y<*%()?DU' =%(D' =%(D' =4@BB3BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*)?D' =0l9 BB A AHCC*<3<*)?D' =0l9 BBHCCBB*<3<*%()?D' =1:B (0.5)*Y3>B ppt_x<*D ' =+4 . B (0.5)0B(#ppt_x)*Y3>B ppt_x<*%()?D' =1:B(#ppt_y+0.4)*Y3>B ppt_y<*D' =+4 . B(#ppt_y+0.4)0B(#ppt_y)*Y3>B ppt_y<*%()?DU' =%(D' =%(D' =4@BB3BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*)?D' =0l9 BB A AHCC*<3<*)?D' =0l9 BBHCCBB*<3<*%()?D' =1:B (0.5)*Y3>B ppt_x<*D ' =+4 . B (0.5)0B(#ppt_x)*Y3>B ppt_x<*%()?D' =1:B(#ppt_y+0.4)*Y3>B ppt_y<*D' =+4 . B(#ppt_y+0.4)0B(#ppt_y)*Y3>B ppt_y<*%()?DP' =%(D' =%(D' =4@BB'BB%()?D' =1:Bvisible*o3>+B#style.visibility<*%(DK' =+4 8?CB#ppt_h/20BCB#ppt_h/20BCB#ppt_hB*Y3>B ppt_h<*DK' =+4 8?CB#ppt_w+.3BCB#ppt_w+.3BCB#ppt_wB*Y3>B ppt_w<*DE' =+ 4 8?CB#ppt_x-.3BCB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*+0  `F(  r  S  Yp`      # 0e0eA%5%6histunifhistogram with uniform PDF <$D 0     # 0e0eA&5%2unifprpluniform probability plot <$D 0  ,    xaxaW?Agora sim...Arial Black"6@ NNN?N.,$D 02  # lxaxa  ?"6@`NNN?NP P @,$D  02  # lxaxa  ?"6@`NNN?NP ,$D  0H  0޽h ? @@))___PPT10l).c7+D@)' = @B D(' = @BA?%,( < +O%,( < +DU' =%(D' =%(D' =4@BB3BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*)?D' =0l9 BB A AHCC*<3<*)?D' =0l9 BBHCCBB*<3<*%()?D' =1:B (0.5)*Y3>B ppt_x<*D ' =+4 . B (0.5)0B(#ppt_x)*Y3>B ppt_x<*%()?D' =1:B(#ppt_y+0.4)*Y3>B ppt_y<*D' =+4 . B(#ppt_y+0.4)0B(#ppt_y)*Y3>B ppt_y<*%()?DU' =%(D' =%(D' =4@BB3BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* )?D' =0l9 BB A AHCC*<3<* )?D' =0l9 BBHCCBB*<3<* %()?D' =1:B (0.5)*Y3>B ppt_x<* D ' =+4 . B (0.5)0B(#ppt_x)*Y3>B ppt_x<* %()?D' =1:B(#ppt_y+0.4)*Y3>B ppt_y<* D' =+4 . B(#ppt_y+0.4)0B(#ppt_y)*Y3>B ppt_y<* %()?D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D|' =%(D' =%(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D' =%(D' =%(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(D ' =%(D ' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(DO' =+4 8?HCBBCBB*k3>'Bstyle.rotation<* %())?DY' =+4 8?dCB#ppt_wBCB#ppt_w*.05B*Y3>B ppt_w<* %())?DY' =+4 8?dCB#ppt_w*.05BCB#ppt_wB*Y3>B ppt_w<* %()?)D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<* DW' =+4 8?bCB#ppt_x+.4BCB#ppt_xB*Y3>B ppt_x<* %())?D]' =+4 8?hCB#ppt_y-.2BCB#ppt_y+.1B*Y3>B ppt_y<* %())?DW' =+4 8?bCB#ppt_y+.1BCB#ppt_yB*Y3>B ppt_y<* %()?)D' =-g6B fade*<3<* %())?+'  P(  r  S X Yp`     S T  Ypv<$  0   H  0޽h ? @@%%___PPT10%.0㦕+R$eD%' = @B D$' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*'%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*'D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*'D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*'A%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*'AD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*'AD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*AG%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*AGD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*AGD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*GO%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*GOD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*GOD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Ob%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*ObD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*ObD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*bo%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*boD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*boD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*o%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*oD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*o+8+0+  +N    q(  r  S Լ Yp`     # 0e0eA5% bootstrabootstrap plots`0PA      f xaxaGH) ?"6@`NNN?NP`0,$D 0 Relativamente disperso,( nK     # l xaxaGrHR ?"6@`NNN?NP0 ,$D  0 Mucho ms concentrado(( nK  P   # xaxa2W?C=.499; CI = [.497,.503]Arial Black"6@`NNN?N0,$D  0P   # xaxa2W?C=.507; CI = [.482,.534]Arial Black"6@`NNN?NH,$D  0H  0޽h ?/    @@___PPT10.`S+sD' = @B Dt' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bplus(in)*<3<* D' =%(D' =%(DB' =A@BBBB0B%(D' =-s6Bwipe(down)*<3<* D' =1:Bhidden*o3>+B#style.visibility<* %(D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(down)*<3<* D' =%(D' =%(DB' =A@BBBB0B%(D' =-s6Bwipe(down)*<3<* D' =1:Bhidden*o3>+B#style.visibility<* %(D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(down)*<3<* D' =%(D' =%(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<* D' =1:Bhidden*o3>+B#style.visibility<* %(D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(down)*<3<* ++0+   ++0+   ++0+   ++0+   +  <(  r  S  Yp`     c $  Y`v<$ 0      r0e0eA7 5%DEDO20<$D  0  H  0޽h ? @@___PPT10.` +CDD' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D:' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*'%(D' =-i6B wedge*<3<*'D' =%(D' =%(D:' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*'K%(D' =-i6B wedge*<3<*'KD' =%(D' =%(D:' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Kd%(D' =-i6B wedge*<3<*KdD' =%(D' =%(D:' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =-i6B wedge*<3<*dDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*+8+0+  +  h(  ~  s * Yp`     s *  Y0<$ 0   H  0޽h ? ̙33^V___PPT106+D' = @B D' = @BA?%,( < +O%,( < +D$' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*<D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*<D' =-g6B fade*<3<*<D$' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*<D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*<D' =-g6B fade*<3<*<D$' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*D' =-g6B fade*<3<*D$' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*D' =-g6B fade*<3<*D$' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*R%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*RD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*RD' =-g6B fade*<3<*R+8+0+  +}  0$(  r  S H fYp`  f r  S  f Yp` f H  0޽h ? @@___PPT10i.* v+D=' = @B +6 ZK0 00p$$l,0(  l l S ~fxaxa1 ?Yp`  f  l S ~fxaxa1 ? Ypv f @.  /  l#  p,$D 0" l c BC DEFb1?,,N4.yl P6A'y ;IWA?|e*Ksl 9) MNY\@- : l c BC*DE<FDA1?tE  "D)_)v( @  . l c BCDEFb!1?""+IcnnzpiyWGv6eD|RyK7.$+  A]0wPEH@ z l c JB CDE\FdA@1?%9 _1rN|[gnRB6*" h 5%/0@* Y3 z  l c JB4CDE\FdA@1? 5 [?sfvyfY)R3F.;!, qSF8 /0@   l c ZB<CDEdFlA@1?<8m`t;_7U-G2)%%&,*S1!34@ ;Z  l c *BCDELFTA@1?\mc.v[K=&8a\'(@(K   l c BCIDEF$___1?H@X  l c BC}DEF?1? & <L*_^{g|m|z /H,gQl|u\5WCAD@   l c B@C~DEFb1?''m%#  P"5F+Zju?R'nGg{}x9o=`>W?N4$em%OP@  2 l c BCJDEFA1?.. 5Da}|\'CID3%g R<iUJDP]_]XXJ)%7 Z&% )1:j8d ]`@&g p l c BCDEFq1?&& o f \ K B 8   *#8yA?4'5Fh&N|j.,MP@ ( * l c B[C2DE4F<1? F2 " .151A1S+ZDF@$ 9z l c JBCwDE\FdA1?n Y 9 9Y l-vHufqieedh /0@ / uJ l c BC|DEDFLq1?|Je{twblDV% )7%fAzJ|J#$@F1  l c B8C+DEF$1?2*7 $2*@5  l c ZBCgDEdFlq1?/+k,S(- -/>PVdbtfx`zWF80/34@ ' l c BCTDE|Fq1? m!Y)O,E,%  #+1(<JL]RgSoSsNrDr;v4. ?@@" v l c jBCXDElFtq1?  [ M+I0A0"&# "")6C L5V?WLUQQQLQFU?& 78@; j  l c ZBC(DEdFlq1?}[K?" &3&=&I't&%$$$%& 34@Z . ?  l c BCC-DE$F,1? , .? B)",@   l c B<C*DE,F41? # )8 ;$!% )#@ - W l c B1C,DE(F01? +"(0 & +@ m0 `B l 01? `B l 0OOO1?; l c BSC_DEF?1?""RR]@z=f=]=S=X\^^lD ),5E#:BCC1'*2=D L  (5REH@ - 2 l c BC-DE8F@A1?H ?* ,*?,V* @ ;R  l c "BC+DEHFPA1? p ` U@6'1(E*]&%(@ ] Z !l c *BC<DELFTA1?kX E:/-%,-(2%40;#;/;F5 '(@g   "l s BNCXDE F(@1?MWS6+?MIk2@ , X #l s (B0CDEHFP@1?/p?lA&U%(@,  $l c RBC6DE`FhA1?k[TLE:%  /4(534R%Zh/x%w  14@E  H l 0޽h ? (O___PPT10+^D|' = @B D7' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*l%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*lD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*l+r   P(  r  S "fYp`  f   S #f Ypv<$ 0 f H  0޽h ? @@ZR___PPT102.f$+n_|D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*'%(D' =-o6Bdissolve*<3<*'D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*'A%(D' =-o6Bdissolve*<3<*'AD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*AX%(D' =-o6Bdissolve*<3<*AXD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Xx%(D' =-o6Bdissolve*<3<*XxD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-o6Bdissolve*<3<*xD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*+8+0+f +   P(  r  S 6fYp`  f   S 7f P<$ 0 f H  0޽h ? @@___PPT10.f+LFDF' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-6B%slide(fromBottom)*<3<*0D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0T%(D' =-6B%slide(fromBottom)*<3<*0TD' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Tb%(D' =-6B%slide(fromBottom)*<3<*TbD\' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*b%(D' =-6B%slide(fromBottom)*<3<*bDR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*D' =%(D^' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*+8+0+f +  P  (    <Ef   f r  S FfYp`  f f  0"` `  c $A |??`  |`  c $A ??  `   c $A ~??& @ ~x   <If 0   " i.e. sf = |a|sx0zzzzzzz2    fl^fxaxa ?"6@`NNN?N0,$D 0 GPero vale slo si la aproximacin lineal es buena en el rango del error6H( K 3 H  0޽h ? @@___PPT10.r +QD;' = @B D' = @BA?%,( < +O%,( < +D-' =%(D' =%(D}' =A@BB1BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* D' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<* D' =-g6B fade*<3<* +8+0+ f +  jb`  (  r  S mfYp`  f   BXnf `  f `   c $A; ??J0    c $A ?? 00 8 $D  0s   0pf@@ H,$ 0 SNuveamente slo es vlida si la aproximacin lineal es buena en el rango del error2T0662 0  6xaxaA     ? A@  A1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab   f'l P   P ,$D 0  0wf"`c @  )OEl coeficiente de correlacin r [-1,+1] es 0 si x,y no estn correlacionadasHP0 /n  B  BHCHDEF38cHPH( ,|X@  "`P 0h  # lȈfxaxa 1?"6@ NNN?N` 9 ,$  0 Z En general& nK H  0޽h ? @@@ 8 ___PPT10 .r@ l+C_D| ' = @B D7 ' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* +p+0+ f ++0+f +    (    <Df Pp f r  S fYp`  f `  c $A ??0 0  `   c $A ??@ y  `   c $A ??      <tf(@ r(slo cranlo& )0`   c $A ??   W   <0f ,$ 0 )El error relativo en x o 1/x es el mismo"*0*HV  0(fzJ,$ 0 *Error en el logaritmo es el error relativo"+0+R H  0޽h ? @@___PPT10.sP+zܤD' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*+p+0+ f ++0+f +Y!    (  r  S fYp`  f   c $fYP<$ 0 f  0 # l0e0eA ?5% ?D0 H $D 0 f 0 C x0e0eA- O?5% ? K H O$D  0 f`  c $A, M??, d  M   Zfxaxa1 ?0 Y ,$  0 ZUso de nmeros complejos  8   Zfxaxa1 ?0 Y`,$ 0 &Problema: hay que estimar incremento  apropiado Alternativa: uso de la derivada exactaXQ8% 8 0 8H  0޽h ? @@___PPT10.4˞+ =*D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DL' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =-{6Bslide(fromTop)*<3<*(D' =%(D' =%(DL' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(G%(D' =-{6Bslide(fromTop)*<3<*(GDL' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*G\%(D' =-{6Bslide(fromTop)*<3<*G\D' =%(DE' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*D' =%(Dl' =%(DN' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-}6B!slide(fromLeft)*<3<* D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 1%(D' =-6B%slide(fromBottom)*<3<* 1D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 1X%(D' =-6B%slide(fromBottom)*<3<* 1X++0+f ++0+ f ++0+ f +N%    (  x  c $fYp`  f   s *fY<$  0 f    v0e0eA<5%STUDENTP6 fH  0޽h ? @@f"^"___PPT10>".4˞+D!' = @B D!' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*;%(D' =-s6Bwipe(down)*<3<*;D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*;Q%(D' =-s6Bwipe(down)*<3<*;QD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Qw%(D' =-s6Bwipe(down)*<3<*QwD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*w%(D' =-s6Bwipe(down)*<3<*wD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*+8+0+f +    n(     0 c 0e0eA ?5% ?"`?H $D 0 fr  S `fYp`  f   c $\f Y<$ 0 f  0 C x0e0eA ?5% ?"`B'H $D  0 fH  0޽h ? @@___PPT10.7@zvP+{D8' = @B D' = @BA?%,( < +O%,( < +D$' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*I%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*ID' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*ID' =-g6B fade*<3<*ID$' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*If%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*IfD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*IfD' =-g6B fade*<3<*IfD$' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*f%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*fD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*fD' =-g6B fade*<3<*fD' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*D' =-g6B fade*<3<*D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* +8+0+f + $  4 ,   (  r  S  Yp`    0  6xaxaA     ? A@  A1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab 0H $D 0    c $ Y`<$  0   ~   Zfxaxa1 ?  ,$  0 VVentajas: Derivada exacta (tampoco hay cociente incremental) Slo hay un cdigo fuente: M < W 8   3 rxaxaA= ? 1?"6@ NNN?N0@ 8 $D 0H  0޽h ? @@~v___PPT10V.5p1:+G pD' = @B Du' = @BA?%,( < +O%,( < +D' =%(D' =%(DT' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*'%(D' =-6B'barn(inHorizontal)*<3<*'D' =%(D' =%(DT' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*'C%(D' =-6B'barn(inHorizontal)*<3<*'CDv' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(DR' =A@BBB%B0B%(D' =1:Bvisible*o3>+B#style.visibility<*  %(D' =-6B%barn(outVertical)*<3<*  D' =%(D' =%(DR' =A@BBB%B0B%(D' =1:Bvisible*o3>+B#style.visibility<*  =%(D' =-6B%barn(outVertical)*<3<*  =D' =%(D' =%(DR' =A@BBB%B0B%(D' =1:Bvisible*o3>+B#style.visibility<* =W%(D' =-6B%barn(outVertical)*<3<* =W+p+0+  ++0+   +)  ~@(  r  S  Yp`     c $  Y`<$ 0      x0e0eA5%j021221900   H  0޽h ? @@&&___PPT10&.-@>b+o%DD&' = @B D%' = @BA?%,( < +O%,( < +D-' =%(D' =%(D}' =A@BB1BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*/%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*/D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*/D' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*/D' =-g6B fade*<3<*/D-' =%(D' =%(D}' =A@BB1BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*/j%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*/jD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*/jD' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*/jD' =-g6B fade*<3<*/jD-' =%(D' =%(D}' =A@BB1BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*j%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*jD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*jD' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*jD' =-g6B fade*<3<*jD-' =%(D' =%(D}' =A@BB1BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*D' =-g6B fade*<3<*D-' =%(D' =%(D}' =A@BB1BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*D' =-g6B fade*<3<*D-' =%(D' =%(D}' =A@BB1BB0B%()?D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =+4 8?HCBCBCBB*k3>'Bstyle.rotation<*D' =-g6B fade*<3<*+8+0+  +  0 (  r  S D) Yp`     c $@*  Yv<$ 0   j   fh. xaxa 1?"6@`NNN?N  Fuente: Vesna Luzar-Stiffler4 nK2    r0e0eA 5%DADOS p  H  0޽h ? @@r j ___PPT10J .l@}+WwD ' = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*3%(D' =-o6Bdissolve*<3<*3D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*3H%(D' =-o6Bdissolve*<3<*3HD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Hq%(D' =-o6Bdissolve*<3<*HqD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*q%(D' =-o6Bdissolve*<3<*q+8+0+  +u   (  r  S A Yp`   r  S B ``P   B   NgֳgֳD?"0@NNN?NB   NgֳgֳD?"0@NNN?N  TH gֳgֳ ?"6@ NNN?N Y0&0 P  TL gֳgֳ ?"6@ NNN?N^ Y1&0 P  Ngֳgֳ?"6@`NNN?NTB  NgֳgֳD?"0@NNN?NTTB  NgֳgֳD?"0@NNN?Nn   Rgֳgֳ    BCsDEF @  5% 8c8c     ?A)BCD|E||| >s>>@  # "0e@       @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abzd n   Rgֳgֳ    BCEDEF @  5% 8c8c     ?A)BCD|E||mL&E6>@  # "0e@       @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab!*  TXP gֳgֳ ?"6@ NNN?N  hp(0.3)=p(1)= ...&0 PH  0޽h ? @@___PPT10i.+D=' = @B +  d(  r  S b Yp`   r  S xc  Y0     # lxaxa Ԕ?"6@`NNN?N  C   fhe xaxa 1?"6@ NNN?N  o2( nK2   E   fo xaxa 1?"6@ NNN?N  q2* nK2 B   fxaxaDԔ?"0@NNN?N  H  0޽h ? @@___PPT10i.*+D=' = @B +>9  x (  r  S  Yp`   r  S   Ypv   >  T, gֳgֳ ?"6@ NNN?Nd},$  0 H^6100 ! 37210000 ! 4410000 ! 16810000 ! 6561000000 P   0O  T gֳgֳ ?"6@ NNN?Np+ ,$  0 Y2&0 PO  T( gֳgֳ ?"6@ NNN?N + ,$  0 Y2&0 PO  TЛ gֳgֳ ?"6@ NNN?N +S ,$  0 Y2&0 PO  T gֳgֳ ?"6@ NNN?N +( ,$  0 Y2&0 P   Tgֳgֳ o?"6@ NNN?N6 G ,$@  0   Tgֳgֳ o?"6@ NNN?N  ,$@  0   Tgֳgֳ o?"6@ NNN?N G ,$@   0   Tgֳgֳ o?"6@ NNN?NG,$D   0   Ngֳgֳ ?"6@ NNN?N% :j,,$@  0z  T gֳgֳ ?"6@ NNN?N   ,$  0 LOOP!80 P(("H  0޽h ? @@f)^)___PPT10>).0p+0D'' = @B D}'' = @BA?%,( < +O%,( < +D"' =%(D"' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* D' =%(Du' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(+P+0+  ++0+  ++0+  ++0+  ++0+  ++0+  +  @ J(  r  S  Y`   r  S p  Yv   B   ZgֳgֳDo?"0@NNN?N@ @0 f    f xaxa  ?"6@`NNN?N0 @\ "A mod B=resto de dividir A entre B*# nK2#" r   Tgֳgֳ ?"6@ NNN?N ,   T gֳgֳ ?"6@ NNN?N  jloop&0 PH  0޽h ? @@___PPT10i. ,W?Tpicamente medias y varianzasArial Black"6@`NNN?N,$D  0H  0޽h ? @@r+j+___PPT10J+.[+YD*' = @B D*' = @BA?%,( < +O%,( < +D' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*0D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*0D' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*0D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*0D' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*=%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*=D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*=D' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*=k%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*=kD' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*=kD' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*k%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*kD' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*kD' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-u6Bwipe(right)*<3<*+8+0+  +}  $(  r  S  Yp`   r  S L  Ypv   H  0޽h ? @@___PPT10i.4`6+D=' = @B +i  ~ (  r  S    G`   4F @  @  N ?@` |Se basa en que" n  c $A/ ~??x ~dz @    @P ,$D  0F  N* ?@ Si X1 y X2 son independientes,V n     c $A1 ?? x dt   N- ?@  ,$  0 Si se pueden generar X1 y X2 de forma que tengan correlacin Cov(X1,X2) negativa puede lograrse que Var(X1+X2) sea menor que si son independientes n  %  #  H  0޽h ? @@  ___PPT10c .`+D ' = @B D ' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* +8+0+   +     (  r  S hA Yp`     c $A3 ??M~7x d  NlX ?@@  Puede ser reformulado como 4   NDb ?P @ donde Xi y Xi estn correlacionados negativamente y las Yi siguen siendo independientesY4    X  c $A4 ??4x x d   c $A: ?? 0 x d   c $A2 ??  x dn   S xaxaW>d?f P 6Pero...cmo?Impact"6@ NNN?N ` H  0޽h ? @@___PPT10i. F6+D=' = @B +   K(  r  S ` Y0     N@w ? 0@,$  0 _Si F(s) es montona (y por lo tanto tambin F-1(s)) entonces X y X tienen correlacin negativa<` n- 1_  TH ?` El procedimiento en general es" n4   T< ?0 P *X=F-1(U) donde U~U(0,1) y dF/ds=f(s):+4  &*J   N̖ ?0 ,$  0 *Pero U~U(0,1) implica que (1-U)~U(0,1)."+ n+*R   T ?   FPor lo que, X=F-1(1-U) tambin tiene la misma distribucin f(s) que X<G n 5FH  0޽h ? @@___PPT10.x+D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DN' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-}6B!strips(upRight)*<3<* D' =%(D' =%(DN' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-}6B!strips(upRight)*<3<*+p+0+  ++0+   +q     S (  r  S 0 Yp`     S ,  Yp0<$  0     c $A5 ??0 am $@  0dz    Pp ,$D  08  N\ ?@ : En ocasiones es fcil resolver analticamente la integral"; n;9   c $A8 ??k@ x dl @   @ ,$D  0E   T ?@   Ky posteriormente hacer la simulacin de Monte Carlo en el residuo, logrando"L nLK   s *A9 ??T cx d  S xaxa$W>d?f P 6No abundaremos...Impact"6@ NNN?N ,$D 0H  0޽h ? @@JB___PPT10".j+ߍD' = @B Dy' = @BA?%,( < +O%,( < +D3' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(down)*<3<* D' =%(D' =%(D`' =4@BB#BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =+4 8?HCB4DBCBB*k3>'Bstyle.rotation<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*+8+0+  +  ~v@ (  r  S  Yp`     c $ P <$ 0      p0e0eA 5%ALTO  H  0޽h ? @@"___PPT10.mF+M@=D' = @B DQ' = @BA?%,( < +O%,( < +D' =%(D' =%(D:' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-i6B wedge*<3<*D' =%(D' =%(D:' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*7%(D' =-i6B wedge*<3<*7D' =%(D' =%(D:' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*7b%(D' =-i6B wedge*<3<*7bD' =%(D' =%(D:' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*b%(D' =-i6B wedge*<3<*bD' =%(D' =%(D:' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-i6B wedge*<3<*D' =%(D' =%(D:' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-i6B wedge*<3<*D' =%(D' =%(D:' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-i6B wedge*<3<*D' =%(D' =%(D:' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-i6B wedge*<3<*+8+0+  +  P(  r  S  Yp`     S  Y00<$  0   H  0޽h ? @@___PPT10.51+NODH' = @B D' = @BA?%,( < +O%,( < +D' =%(D+' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*7%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*7D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*7D' =%(D+' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*7[%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*7[D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*7[D' =%(D+' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*[y%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*[yD' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*[yD' =%(D+' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*y%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*yD' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*yD' =%(D+' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D+' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*+8+0+  +,  P dP(  dr d S < 2 Yp`  2   d S 8 2 Y<$  0 2  H d 0޽h ? @@u*m*___PPT10M*.=@+D)' = @B D)' = @BA?%,( < +O%,( < +D' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*dD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*dD' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*d2%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*d2D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*d2D' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*d2T%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*d2TD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*d2TD' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*dTg%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*dTgD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*dTgD' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*dg~%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*dg~D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*dg~D' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*d~%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*d~D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*d~D' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*dD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*dD' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*dD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*dD' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*dD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*d+8+0+d  +pZK0 w(    S ~9 xaxa1 ?p     S ~0 xaxa1 ? Z@   "    `` xaxa1?   }carlos.lopez@ieee.org*0   H  0޽h ? (Oy___PPT10Y+D=' = @B +  0 {(  X  C    {  S Pv  @   Tomado de Computational Statistics Course Vesna Luzar-Stiffler, Ph.D. University of Zagreb and CAIR Research Center Zagreb, Croatia vesna.luzar-stiffler@cair-center.hr Computational Statistics Course Part IMonteCarloBootstrap.ppt* H  0޽h ? a(80___PPT10.  Z 0 (  X  C      S x  @   jEl primer grfico (arriba, izquierda) es de los datos vs. Su ndice. El segundo (arriba, derecha) es de un dato vs. el siguiente. 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Carlos Lpezem73 Microsoft PowerPoint 4.0lat@ S@g]E@&.v@`1# A GSg  )'    """)))UUUMMMBBB999|PP3f333f3333f3ffffff3f̙3ff333f333333333f33333333f33f3ff3f3f3f3333f33̙33333f333333f3333f3ffffff3f33ff3f3f3f3fff3ffffffffff3ffff̙fff3fffff3fff333f3f3ff3ff33f̙̙3̙ff̙̙̙3f̙3f333f3333f3ffffff3f̙3f3f3f333f3333f3ffffff3f̙3f3ffffffffff!___www4'A x(xKʦ """)))UUUMMMBBB999|PP3f3333f333ff3fffff3f3f̙f3333f3333333333f3333333f3f33ff3f3f3f3333f3333333f3̙33333f333ff3ffffff3f33f3ff3f3f3ffff3fffffffff3fffffff3f̙ffff3ff333f3ff33fff33f3ff̙3f3f3333f333ff3fffff̙̙3̙f̙̙̙3f̙3f3f3333f333ff3fffff3f3f̙3ffffffffff!___wwwݥ՜.+,0     + Presentacin en pantallaoi_: mArial Book AntiquaMonotype SortsTimes New Roman WingDingsSymbolVerdana Arial NarrowTahoma toplinecMicrosoft Equation 3.0#Microsoft Editor de ecuaciones 3.0 Bitmap Image#Hoja de clculo de Microsoft Excel Mdulo 3: Midiendo la ExactitudPlanError, Exactitud y PrecisinDefiniendo estndares1: qu exigir2: entrenar a la gente#3: verificar procesos y resultadosPlanInformando sobre la CalidadPlanMidiendo y VerificandoCualquiera sea el test Veremos unoNSSDA Siete pasosSiete pasos (cont) Siete pasos Siete pasosAlgunos detalles Siete pasosDatos independientes?Siete pasos (cont)Clculos en horizontalClculos en la vertical"Variables temticas o categricasCmo medir la Exactitud?Alguna terminologaResultados del ejemploLa tabla completaEl ndice kappa de Cohen Ejemplo:Ejemplo (cont.):Un pequeo problemaDigresin: Midiendo CalidadOtras componentesEjemplo: Coherencia lgicaVolviendo a los Siete pasosDeclaracin de ExactitudIncluyendo la IncertidumbreIncluyendo Incertidumbre(2)Siete pasos (cont) ComunicandoOtras formas de estimarDiapositiva 44Porqu Remuestrear? BootstrapEjemploDiapositiva 48Diferencia promedioEstimadores corrientesIntervalo de Confianza CIMedia y varianza de la muestraMuestreo con ReemplazoCalculando nuevos CI Y entonces?Diapositiva 56ProcedimientoProcedimiento(2) Atencin:Otro ejemplo:Qu hacer primero? 4 grficosSupongamos UniformeUn estimador para CCmo lucen los CI ImportanciaOtros mtodos de remuestreoRecapitulando:PlanAnlisis de SensibilidadCuanto antes mejorEjemplo analtico 1Ejemplo analtico 2Otras frmulas analticas En generalDerivada exactaGeneradores de cdigoSobrecarga de operadoresEn qu andbamos?Mtodos de Monte CarloLa parte aleatoriaNmeros seudo-aleatoriosSeudo-Aleatorios*Linear congruential method (Lehmer, 1948)Familia popularPara PDFs no uniformesSimulacin de Monte CarloAlgunos problemasTRV: Enfoque AntitticoEjemplo: Integral (o promedio)#Cmo lograr correlacin negativa?Otros trucosAspectos importantes en SMC En resumen:Cmo medir Sensibilidad? Mdulo 3: Midiendo la Exactitud Fuentes usadas Plantilla de diseoServidores OLE incrustadosTtulos de diapositiva_-_  Dr. Ing. Carlos LpezDr. Ing. Carlos Lpez  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./012345789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`bcdefghjklmnopRoot EntrydO)PicturesxCurrent UseriSummaryInformation(6UPowerPoint Document(=1 DocumentSummaryInformation8a