On Charlier polynomials in testing Poissonity

ABSTRACT

This article discusses applications of Charlier polynomials when checking how well classic Poisson model fits the data. We show that smooth components pertaining to the polynomials can be effectively used in preliminary analysis of data at hand and we propose and discuss some tests based on them. Our extensive simulations shed new light on power behavior of the best tests in the area.

KEYWORDS:

• Diagnostic test
• Fisher's index of dispersion
• Goodness of fit
• Parametric bootstrap
• Poisson distribution
• Power comparison
• Selection rule
• Smooth test

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F03

Acknowledgments

The authors are very grateful to a reviewer for the insightful comments that led to the improvement of the presentation. The authors also thank Prof. C. C. Kokonendji for an off-print of his article.

Funding

This work was supported by Grant N N201 608440 from the National Science Centre, Poland. Calculations have been carried out in Wrocław Centre for Networking and Supercomputing (http://www.wcss.wroc.pl), grant No. 199.