Geodesic
Binomial-$\chi^2$ vector random fields
Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 3, pp. 547-562 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: $\chi^2$ vector random fields, Gaussian vector random fields, elliptically contoured vector random fields, covariance matrix function. 
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Ch. Ma. Binomial-$\chi^2$ vector random fields. Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 3, pp. 547-562. http://geodesic.mathdoc.fr/item/TVP_2016_61_3_a5/

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