On new tests of fit for the geometric distribution based on a characterisation

Abstract

The geometric distribution is used in multiple research fields across various disciplines. Therefore, it is important to be able to test the assumption of whether a set of observed data arises from this distribution. The purpose of this dissertation is to review the literature on existing goodness-of-fit tests for the geometric distribution and to develop new goodness-of-fit tests based on a mean residual life characterization of the geometric distribution. The first test is a Kolmogorov-Smirnov type test, and the second and third tests are Cramér-von Mises type tests, with empirical and parametric weight functions, respectively. We compare the performance of these tests with existing goodness-of-fit tests for the geometric distribution in a Monte Carlo simulation study. These tests are compared considering several alternative distributions including mixture distributions to analyze the estimated powers. Lastly, the tests are applied to observed data. Considering the power performance of our tests, it is clear that these tests match or outperform the majority of existing tests considered in this study against the alternatives considered.