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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Variogram ： ウィキペディア英語版 Variogram In spatial statistics the theoretical variogram $2\backslash gamma(x,y)$ is a function describing the degree of spatial dependence of a spatial random field or stochastic process $Z(x)$. For instance in mining a variogram will give a measure of how much two samples taken from the mining area will vary in gold percentage depending on the distance between those samples. Samples taken far apart will vary more than samples taken close to each other. ==Definition== The variogram is defined as the variance of the difference between field values at two locations ($x$ and $y$) across realizations of the field (Cressie 1993): :$2\backslash gamma(x,y)=\backslash text\backslash left(Z(x)\; -\; Z(y)\backslash right)\; =\; E\backslash left(-\; \backslash mu(y)))^2\backslash right).$ If the spatial random field has constant mean $\backslash mu$, this is equivalent to the expectation for the squared increment of the values between locations $x$ and $y$ (Wackernagel 2003) (where $x$ and $y$ are not coordinates but points in space): :$2\backslash gamma(x,y)=E\backslash left()\; ,$ where $\backslash gamma(x,y)$ itself is called the semivariogram. In the case of a stationary process, the variogram and semivariogram can be represented as a function $\backslash gamma\_s(h)=\backslash gamma(0,0+h)$ of the difference $h=y-x$ between locations only, by the following relation (Cressie 1993): :$\backslash gamma(x,y)=\backslash gamma\_s(y-x).$ If the process is furthermore isotropic, then the variogram and semivariogram can be represented by a function $\backslash gamma\_i(h):=\backslash gamma\_s(h\; e\_1)$ of the distance $h=\backslash |y-x\backslash |$ only (Cressie 1993): :$\backslash gamma(x,y)=\backslash gamma\_i(h).$ The indexes $i$ or $s$ are typically not written. The terms are used for all three forms of the function. Moreover, the term "variogram" is sometimes used to denote the semivariogram, and the symbol $\backslash gamma$ is sometimes used for the variogram, which brings some confusion. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Variogram」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.