A New Table of Percentage Points of the Pearson Type III Distribution

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Abstract
Recently the U. S. Water Resources Council has proposed standardization of the analysis of peak flood discharges by fitting a Pearson Type III distribution to the logarithms of the data. This action has served to draw attention to the inadequacy of available tables of percentage points of the Pearson Type III distribution and the need for better tables. Many tables of percentage points of the related chi-square distribution are available in the literature, perhaps the most comprehensive being those published by the author in 1964. These could be used to obtain percentage points of the Pearson Type III distribution, but it would be much more convenient to have a table from which percentage points of the latter distribution could be read directly for uniformly spaced values of the skewness coefficient. The author has therefore, by a modification of the programs used to compute his 1964 tables of percentage points of the chi-square distribution, obtained percentage points, corresponding to cumulative probability P = .OOOl, .0005, .OOl, .005, .Ol, .02, .025, .04, .05, .1(.1).9, .95, .96, .975, .98, .99, .995, .999, .9995, .9999, of the standardized Pearson Type III distribution with skewness α3 ≡ = 0.0(0.1)9.0. This paper includes the five-decimal-place table, accurate to within a unit in the last place, together with a description of the method of computation and a discussion of possible applications, including the estimation of the return periods of floods. Space has been conserved by giving results only at intervals of 0.2 in α3 for α3 > 4.8; the intermediate values, if needed, can be obtained by interpolation.

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