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

Abstract

In this paper we develop an efficient analytical expansion of the cumulative distribution function (cdf) X B X 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.