(iii) Let [x.sub.3,3] denote the quality of the

covariance function used to model the network correlation errors.

Since the power variogram does not have a finite sill and integral scale and lacks an explicit form of

covariance function, the SGSIM module in GSLIB does not have the support to use power variogram.

For each eigenfunction, a specific eigenvalue is associated as the first two eigenvalues for additive genetic and permanent environmental effects account for more than 98% of the total variation while the first three eigenvalues of the additive genetics and permanent

covariance function accounted for at least 99.5% of the variations.

The fundamental information about the spectral quantity, that it must vanish at a lower and upper spectral limit, can be stated by the

covariance function of a Brownian bridge process as described in Section 4.

On the other hand, Bohorquez (2010) conducted and analysis for predictive purposes the presence of PM10 in Bogota by using a non-separable

covariance function, resulting in a predictive model of distribution space in the presence of PM10.

A Brownian stochastic flow {x(u, t), u [member of] R, t [greater than or equal to] 0} is called a Harris flow with

covariance function r if for any u, v [member of] R the joint quadratic variation of the martingales {x(u, t), t [greater than or equal to] 0} and {x(v, t), t [greater than or equal to] 0} is given by

The elements of this matrix are determined with a suitable

covariance function. Thus, the

covariance functions of the signals are determined empirically with the help of the

covariance functions.

The dependency can be specified via an arbitrary

covariance function or kernel k([x.sub.p], [x.sub.q]).

A GP is completely specified by its mean function and

covariance function. The mean function m(X) and the

covariance function k(X,X') of a real process f(X) are defined as below:

The sample

covariance function of f(x) = [[f.sub.1](x), [f.sub.2](x), ..., [f.sub.n](x)], x [member of] [[x.sub.1], [x.sub.p]] is given by

Assume that K(x) = K(x, [omega]) is a Gaussian log-normal field with known

covariance function C(x, y).