An exact Kolmogorov–Smirnov test for the Poisson distribution with unknown mean

Abstract

We develop an exact Kolmogorov–Smirnov goodness-of-fit test for the Poisson distribution with an unknown mean. 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. Exact critical values are obtained using a new algorithm. We explore properties of the test, and we illustrate it with three examples. The new test seems to be the first exact Poisson goodness-of-fit test for which critical values are available without simulation or exhaustive enumeration.

Keywords:

• conditional test
• Cramér–von Mises statistics
• goodness of fit
• multinomial distribution

Acknowledgements

The author wishes to thank the referee for helpful comments on the paper.