Proportional Effect

Consider two neighborhoods of quasi-stationarity $V({/boma x}_0)$ and $V({/boma x}'_0)$ centered on the two different points ${/boma x}_0$ and ${/boma x}'_0$. Let $/gamma({/boma h}, {/boma x}_0)$ and $/gamma({/boma h}, {/boma x}'_0)$ be the semi-variograms defined on these two neighborhoods.

Quite often, in practice, in mining applications, these two semi-variograms can be made to coincide after multiplication by a factor which is a function of the ratio of the experimental means, $/hat{m}({/boma x}_0)$ and $/bar{m}({/boma x}'_0)$, of the available data in $V({/boma x}_0)$ and $V({/boma x}'_0)$. This amounts to assuming that there exists a stationary model $/gamma_0({/boma h})$ independent of the neighborhood $V({/boma x}_0)$ and such that

thus,

The experimental mean $/hat{m}({/boma x}_0)$ is an estimator of the expectation $E/{Z({/boma x})/} = m({/boma x}_0)$, which is constant over the neighborhood of quasi-stationarity $V({/boma x}_0)$. The two quasi-stationarity models $/gamma({/boma h}, {/boma x}_0)$ and $/gamma({/boma h}, {/boma x}'_0)$ are said to differ from each other by a proportional effect.