Tests of Fit for the Geometric Distribution

Abstract

This article gives power comparisons of some tests of fit for the Geometric distribution. These tests include a Chernoff–Lehmann X ² test, some smooth tests, a Kolmogorov–Smirnov test, and an Anderson–Darling test. This article suggests that a good test of fit analysis is provided by a data dependent Chernoff–Lehmann X ² test with class expectations greater than unity, and its components. These data dependent statistics involve arithmetically simple parameter estimation, convenient approximate distributions, and provide a fairly complete assessment of how well the data agrees with a Geometric distribution. The power comparisons indicate also that the best performed single statistic is the Anderson–Darling statistic.

Keywords:

• Diagnostic test
• Dispersion test
• Empirical distribution function
• Partition of X ²

Acknowledgment

We wish to thank a referee for a number of helpful comments.