Distribution of a Sum of Weighted Noncentral Chi-Square Variables

Abstract

We derive Laguerre expansions for the density and distribution functions of a sum of positive weighted noncentral chi-square variables. The procedure that we use is based on the inversion of Laplace transforms. The formulas so obtained depend on certain parameters, which adequately chosen will give some expansions already known in the literature and some new ones. We also derive precise bounds for the truncation error