ASAS/IMLMacro for Computing Percentage Points of Pearson Distributions

Abstract

The Pearson distribution family provides approximations to a wide variety of observed distributions using the first four moments or the first three moments with a left or right boundary. Curve fitting utilizing Pearson distributions has been extensively applied in many fields. However, in practice, it is quite unwieldy to obtain percentage points of Pearson distributions when consulting the massive tables of Pearson and Hartley (1972) or using the out-of-date computer programs (Amos and Daniel 1971; Bouver and Bargmann 1974; Davis and Stephens 1983). The present study compiled a convenient computer program for computing the percentage points using the contemporary SAS/IML (SAS Institute Inc. 2008) macro language.

Computing and graphing probability values of pearson distributions: a SAS/IML macro

“…There are both extant, old-fashioned in-print tables [4] and contemporary computer programs [5–9] that provided a means of obtaining percentage points of Pearson distributions corresponding to certain pre-specified percentages (or probability values; e.g., 1.0%, 2.5%, 5.0%, etc.). Unfortunately, they are little useful in statistical analysis because we have to employ unwieldy second difference interpolation for both skewness √ β 1 and kurtosis β 2 to calculate a probability value of a Pearson distribution corresponding to a given percentage point, such as an observed test statistic in hypothesis testing.…”

Computing and Graphing Probability Values of Pearson Distributions: A SAS/IML Macro

“…Thus, Pearson distributions made statistical analysis possible for data with unknown distributions. There are both extant old-fashioned in-print tables (Pearson and Hartley, 1972) and contemporary computer programs (Amos and Daniel, 1971;Bouver and Bargmann, 1974;Bowman and Shenton, 1979;Davis and Stephens, 1983;Pan, 2009) available for obtaining percentage points of Pearson distributions corresponding to certain pre-specified percentages (or probability values) (e.g., 1.0%, 2.5%, 5.0%, etc. ), but they are little useful in statistical analysis because we have to rely on unwieldy second difference interpolation to calculate a probability value of a Pearson distribution corresponding to any given percentage point, such as an observed test statistic in hypothesis testing.…”