New Goodness-of-Fit Test for the Gamma Distribution Based on Sample Spacings fromComplete and Censored Samples

摘要

This thesis studies a new goodness-of-fit test for the gamma distribution withknown shape parameter. This test statistic, Z*, is based on spacings from complete or censored samples. The size of samples varied between 5 and 35. The critical value tables were generated for the Z* test statistic for complete and censored samples. The critical values were obtained for five different significance levels: 0.20 0.15, 0.10, 0.05, and 0.01. An extensive power study, containing 50,000 Monte Carlo runs was conducted using nine alternative distributions, H(a). It was observed that the Z* test statistic was more powerful against certain alternatives which are less skewed than the gamma distribution with a given shape parameter. A regression between the critical values and the sample size, shape parameter, significance levels and degree of censoring was established. The power of the Z* test statistic is compared to the powers of the competing test statistics (K-S, W sub 2, and A-D). This thesis reveals that the Z* test statistic is a directional test. This feature may be utilized to attain higher power values by coupling the Z* and the A-D test statistics in a sequential test. (AN).