An Exact Kolmogorov–Smirnov Test for the Logarithmic Series Distribution with Unknown Parameter

Abstract

Abstract
In this paper, we develop an exact Kolmogorov–Smirnov goodness-of-fit test in the case of logarithmic series distribution with an unknown parameter value. This test is conditional, with the test statistic being the maximum absolute difference between the empirical distribution function and its conditional expectation given the sample total. Some modifications are done on an algorithm previously proposed in the case of the Poisson distribution and used the modified algorithm for obtaining the exact critical values. We illustrate the test with three examples. We also include some simulations in order to investigate the power of the procedures. The new test seems to be the first exact goodness-of-fit test for logarithmic series distribution for which critical values are available without simulation or exhaustive enumeration.

Keywords: conditional test; Cramér–von Mises statistics; Anderson-Darling statistics; goodness of fit