Quadratic forms in spherical random variables: Generalized noncentral x2 distribution

T. Cacoullos and M. Koutras

Naval Research Logistics Quarterly, 1984, vol. 31, issue 3, 447-461

Abstract: Let X denote a random vector with a spherically symmetric distribution. The density of U = X'X, called a “generalized chi‐square,” is derived for the noncentral case, when μ = E(X) ≠ 0. Explicit series representations are found in certain special cases including the “generalized spherical gamma,” the “generalized” Laplace and the Pearson type VII distributions. A simple geometrical representation of U is shown to be useful in generating random U variates. Expressions for moments and characteristic functions are also given. These densities occur in offset hitting probabilities.

Date: 1984
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Persistent link: https://EconPapers.repec.org/RePEc:wly:navlog:v:31:y:1984:i:3:p:447-461

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