The use of transformations to find the probability integral of chi-square

The objective of this study is to compute a transformation which is characterized by both accuracy and ease of computation, needs no interpolation, and is normalized. In the attempt to achieve these objectives, some of the properties of the chi-square distribution are summarized, some of the uses of chi-square are shown, and some of the transformations of chi-square are examined on the basis of the criteria of the paper. Transformations by Aroian, Cornish-Fisher, Fisher, Haldane, Pelser, and Wilson and Hilferty are examined and compared with the exact values of the percentage points of chi-square.