Cumulative distribution function of the sum of correlated chi— squared random variables

The cumulative distribution function of the sumS, of correlated random variables can be obtained by considering a multivariate generalization of a gamma distribution which occurs naturally within the context of a general multivariate normal model. By application of the inversion formula to the characteristic function of S, an accurate method for calculating the distribution of S was obtained. An explicit expression for this distribution is presented for certain parameter values in the case where the underlying multivariate normal model has the moving averages correlation structure. Agreement between the two methods was excellent.