Sharp estimates for the CDF of quadratic forms of MPE random vectors

Authors:
J. Sadefo Kamdem
Affiliations:
Université de Montpellier 1, LAMETA (UMR 5474 - CNRS), 3, Avenue de la Mer Richter, 34000 Montpellier, France
Venue:
Journal of Multivariate Analysis
Year:
2010

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Abstract

In this paper we develop an efficient analytical expansion of the cumulative distribution function (cdf) XBX^t where X=(X"1,...,X"n"+"1) with n=2, follows a multivariate power exponential distribution (MPE). Our approach provides a sharp estimate of the cumulative distribution function of a quadratic form of MPE, together with explicit error estimates.