On the representation and computational aspects of the distribution of a linear combination of independent noncentral chi-squared random variables

This article presents two new results relevant to a linear combination of χ² random variables. The first result expresses the cumulative distribution function as a simple multiple of a certain tilted density. The second result shows that in important cases the inversion integral for the density may be expressed as a sum of relatively simple real integrals which, using suitable numerical methods, are straightforward to compute quickly and accurately.