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Biometrika 1986 73(2):528-532; doi:10.1093/biomet/73.2.528
© 1986 by Biometrika Trust
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Miscellanea

On the generalized noncentral chi-squared distribution induced by an elliptical gamma law

MARKOS KOUTRAS

Statistical Unit, University of Athens Panepistemiopolis, Athens 157 10, Greece

Certain important statistical inference and classification problems lead to the consideration of quadratic forms in rotationally invariant random variables. In this paper noncentral probabilities under a multivariate elliptical gamma distribution are studied. The density and cumulative distribution function of the squared noncentral radii are expressed in a Laguerre series form and certain recurrences are derived. Finally, two numerical approximations are discussed.

Key Words: Elliptical gamma distribution • Generalized noncentral chi-squared distribution • Laguerre series forms


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