(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).