Modified Kolmogorov-Smirnov, Anderson-Darling, and Cramer-Von Mises Tests for the Pareto Distribution with Unknown Location and Scale Parameters

摘要

This thesis develops goodness-of-fit tests for the Pareto distribution by generating critical value tables for the modified Kolmogorov-Smirnov, Anderson-Darling, and Cramer-von Mises statistics. These tables can be used to test whether a set of observed values follows a Pareto distribution when the location and scale parameters are unspecified and must be estimated from the observed sample data. Additionally, the power of each of the three goodness-of-fit tests is studied and compared. Finally, the functional relationship between the critical values and the Pareto shape parameter is determined. Keywords: Monte Carlo method; probability distribution functions; statistical analysis; statistical decision theory; statistical tests; order statistics; Air Force equipment; computer programs.