Comparisons of the Percentage Points of Distributions with the Same First Four Moments, Chosen from Eight Different Systems of Frequency Curves

Abstract
A study was made of the extent to which the probability integrals of members of different systems of univariate, unimodal frequency curves, y = f(x), having identical first four central moments, are in agreement. If the variables, x, are standardized so as to have a zero mean and unit standard deviation, it is possible to investigate to what extent the two shape parameters, often described as measuring skewness and kurtosis, can provide estimates for several different systems of distributions, of the probability integrals. This report presents the results of this study.

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