Distribution of a Sum of Weighted Chi-Square Variables

This paper discusses how to obtain percentage points of the distribution of a sum of k weighted chi-square variables. A table of points is given for selected weights, for k 6, 8, 10 existing tables are for k or 5. The new points have been calculated by a technique of Imhof which gives very accurate values but is expensive in computer time. Therefore two new approximations are considered a Pearson curve fit using four moments and a chi-square fit using three. Both give excellent results in the upper tail, the tail usually needed for practical applications the chi-square fit appears superior to other approximations in the lower tail.