RESEARCH ARTICLE


Specification Tests for the Poisson Distribution with a Stochastic Parameter



Simos G. Meintanis*
Department of Economics, National and Kapodistrian University of Athens, Athens, Greece.


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© 2011 G. Meintanis et al.;

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Economics, National and Kapodistrian University of Athens, Athens, Greece. Tel: ++302103689814; E-mail: simosmei@econ.uoa.gr


Abstract

A new method is proposed for testing the mixed Poisson model which employs the well known identity between the probability generating function of the mixed Poisson distribution and the Laplace transform of the mixing distribution. The method utilizes a weighted L2-type statistic which may be easily calculated and the resulting test is consistent against general alternatives. A limit statistic is shown to be related to earlier methods which employ moment-- based contrasts. Some simulation results are also shown.

Keywords: Goodness-of-fit test, Probability generating function, Laplace transform, Mixed Poisson distribution..