Bora H. Onen

Date of Award


Document Type


Degree Name

Master of Science


Department of Operational Sciences

First Advisor

Albert H. Moore, PhD


Kolmogorov-Simirnov and the Kuiper goodness-of-fit tests are studied for the Cauchy distribution with the unknown location and scale parameters. Monte Carlo simulation studies were performed using maximum likelihood estimation to calculate the critical values for standard Kolmogorov-Simirnov and the Kuiper tests. Then a reflection technique is introduced and the critical value tables are calculated for both the Reflected Kolmogorov-Simirnov and the Reflected Kuiper tests. Several sequential tests are performed by combining standard Kolmogorov-Simirnov and Kuiper in one test, standard Cramer-von Mises and the standard Kuiper in the other and finally the reflected Cramer-von Mises and the standard Kuiper in the last one. The Monte Carlo simulations used 50000 repetitions for sample sizes of 5 through 50 with increment of 5. Throughout the study the location parameter is taken as 0 while the scale parameter is kept at 10. Power studies corresponding to each case are done and the results are presented in tables. The power studies are performed for sample sizes 5 through 50 and for α = 0.01, 0.05, 0.10, 0.15, 0.20 for the standard and the reflected tests. For sequential tests power studies have been accomplished for all of the significance level produced by combining two individual tests at form α = 0. 01 to 0.20 with the increment of 0.01. The Kuiper test turns out to have an overwhelming power against all distributions in standard case.

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