A mixture approximation to the distribution of a weighted sum of chi-squared variables

Abstract

The problem of Computing the Values of the distribution functions of linear combinations of chi-squared random variables and their percentile points was previously studied by Grad and Solomon (1955), Imhof (1961). Jensen and Solomon (1972). Solomon and Stephens (1977) and others. All the methods available in the literature either demand lengthy computations or are insufficiently accurate. In the present paper a new method is proposed which reduces the amount of needed computations and yet yields sufficiently accurate results.