Binomial-chi(2) vector random fields

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We introduce a new class of non-Gaussian vector random fields in space and/or time, which are termed binomial-chi(2) vector random fields and include chi(2) vector random fields as special cases. We define a binomial-chi(2) vector random field as a binomial sum of squares of independent Gaussian vector random fields on a spatial, temporal, or spatio-temporal index domain. This is a second-order vector random field and has an interesting feature in that its finite-dimensional Laplace transforms are not determined by its own covariance matrix function, but rather by that of the underlying Gaussian one. We study the basic properties of binomial-chi(2) vector random fields and derive some direct/cross covariances, which are based on the bivariate normal density, distribution, and related functions, for elliptically contoured and binomial-chi(2) vector random fields.