Logistic vector random fields with logistic direct and cross covariances

Abstract

Elliptically contoured random field Gaussian random field Isotropic Logistic distribution Spherically invariant random field Stationary Variogram a b s t r a c tThe logistic vector random field is introduced in this paper as a scale mixture of Gaussian vector random fields, and is thus a particular elliptically contoured (spherically invariant) vector random field. Such a logistic vector random field is characterized by its mean function and covariance matrix function just as in the case of Gaussian vector random fields, and so it is flexible enough to allow for any possible mean structure or covariance matrix structure. We also derive covariance matrix functions whose direct and cross covariances are of the logistic type.

Covariance Models for Multivariate Random Fields resulting from Pseudo Cross-Variograms

“…In fact, the matrix-valued kernels g = (g ij ) i,j=1,...,m given there are exactly the positive conditionally negative definite matrixvalued kernels as introduced in Section 2. Similarly, various other cross-covariances in Ma (2013) and Balakrishnan et al (2015), for instance, can be generalized by replacing the variogram used there with a pseudo cross-variogram.…”

Multifractional Vector Brownian Motions, Their Decompositions, and Generalizations

“…More precisely, we introduce three types of covariance matrix structures for Gaussian or elliptically contoured vector random fields in space and/or time, which are the generalized forms of (multi-, bi-, tri-)fractional vector Brownian motions and related stochastic vector processes. The reader is referred to [41, 42, and 60] for the definition, basic properties, and applications of elliptically contoured (spherically invariant) scalar or vector random fields, which include Gaussian, Student's t, stable, logistic [9], hyperbolic [21], Mittag-Leffler, Linnik, and Laplace vector random fields as special cases.…”

$K$-differenced vector random fields

“…MatLab code for generating a visual figure for rejection sampling of the distribution rand('seed',56789); x = -6:.001:6; alpha1=3.7; %params(1); alpha2=12. 19; %params (2); C=log(alpha1)-log(alpha2); lambda=((alpha2^(-1)-alpha1^(-1))/(log(alpha1)-log(alpha2)))^(.5); % The density of the K-Differenced random variable f(x) f = @(x)(exp(-lambda*(2*alpha2)^(0.5)*abs(x))-exp(-lambda*(2*alpha1)^(.5)*abs(x)))./(C.*abs(x)); t = plot(x,f(x),'b','linewidth',2); hold on; % Proposal double exponential or laplace distribution g(x) g = @(x)(1/2)* exp(-abs(x)); c = max(f(x)./g(x)); %scaling constant c = max(f(x)./g(x)) a = plot(x,c*g(x),'k--'); % plot of the scaled proposal the envelop distribution c*g(x). The following is an m.file to generate random number from the K-differenced random variable.…”