A Modified Kolmogorov-Smirnov, Anderson-Darling, and Cramer-Von Mises Test for the Cauchy Distribution with Unknown Location and Scale Parameters.

The Kolmogorov-Smirnov, Anderson-Darling, and Cramer-von Mises critical values are generated for the Cauchy distribution. The critical values are used for testing the null hypothesis that a set of observations follow a Cauchy distribution when the location and scale parameters are unknown and estimated from the sample. A Monte Carlo simulation, using 5000 repetitions, was used to generate the critical values for sample sizes of 5(5)30 and 50. A power study was performed using Monte Carlo simulation for the Kolmogorov-Smirnov, Anderson-Darling, and Cramer-von Mises goodness of fit tests. Sample sizes of 5, 15, 25 and 50 were used for six alternate distributions, for alpha levels of .05 and .01. Analyzing by sample size shows very poor power for a sample size of five. As the sample size increases so does the power, so that at a sample size of fifty, the powers against three of the six distributions is .5 or better. Among the three tests, the Kolmogorov-Smirnov is consistently more powerful, regardless of sample size or alpha level. Keywords: Theses; and Hypothesis testing. (Author)