New inference procedures for generalized Poisson distributions

Abstract

A common feature for compound Poisson and Katz distributions is that both families may be viewed as generalizations of the Poisson law. In this paper, we present a unified approach in testing the fit to any distribution belonging to either of these families. The test involves the probability generating function, and it is shown to be consistent under general alternatives. The asymptotic null distribution of the test statistic is obtained, and an effective bootstrap procedure is employed in order to investigate the performance of the proposed test with real and simulated data. Comparisons with classical methods based on the empirical distribution function are also included.

Keywords:

• empirical probability generating function
• compound Poisson distribution
• goodness-of-fit test
• Katz laws

AMS Subject Classification:

• 62G10
• 62G20

Acknowledgements

The author wishes to sincerely thank the referees for the constructive criticism that led to improvement of the paper.

Additional information

Notes on contributors

Simos G. Meintanis

Email: [email protected]