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

• Activity Number: 33
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Wei Pan*+ and John C. Boling
• Companies: Duke University and Duke University
• Keywords: Pearson distributions ; nonparametric statistics ; curve fitting

Abstract

Any empirical data can be nonparametrically fitted to one of Pearson distributions using the first four moments (Elderton & Johnson, 1969; Ord, 1972; Pearson, 1895). Pearson and Hartley's (1972) tables as well as the existing computer programs (e.g., Amos & Daniel, 1971; Bouver & Bargmann, 1973; Davis & Stephens, 1983; Pan, 2009) provide a means of obtaining percentage points of Pearson distributions but for only certain pre-specified percentages or probability values (e.g., 1.0%, 2.5%, ., 99.0%). To obtain a percentage point of Pearson distributions for any given probability value, other than the pre-specified probability values, researchers often have to rely on unwieldy second difference interpolation. Conversely, the same problem also exists in obtaining a probability value of Pearson distributions for any given percentage point. Thus, the present study develops a SAS/IML Marco to compute and graph probability values of Pearson distributions for any given percentage point so as to facilitate researchers to conduct nonparametric statistical analysis or testing that requires obtaining probability values of Pearson distributions for any given percentage points.