High Quality Content by WIKIPEDIA articles! In spatial statistics the theoretical variogram 2?(x,y) is a function describing the degree of spatial dependence of a spatial random field or stochastic process Z(x). It is defined as the expected squared increment of the values between locations x and y (Wackernagel 2003): 2gamma(x,y)=Eleft(|Z(x)-Z(y)|^2right) , where ?(x,y) itself is called the semivariogram. In case of a stationary process the variogram and semivariogram can be represented as a function ?s(h) = ?(0,0 + h) of the difference h = y ? x between locations only, by the following relation (Cressie 1993): ?(x,y) = ?s(y ? x). If the process is furthermore isotropic, then variogram and semivariogram can be represented by a function ?i(h): = ?s(he1) of the distance h=|y-x| only (Cressie 1993): ?(x,y) = ?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 for semivariogram and the symbol ? for the variogram, which brings some confusion.

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