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Testing Poissonity of a large number of populations

Author

Listed:
  • M. D. Jiménez-Gamero

    (Universidad de Sevilla)

  • J. de Uña-Álvarez

    (CINBIO, Universidade de Vigo, SiDOR Research Group)

Abstract

This paper studies the problem of simultaneously testing that each of k samples, coming from k count variables, were all generated by Poisson laws. The means of those populations may differ. The proposed procedure is designed for large k, which can be bigger than the sample sizes. First, a test is proposed for the case of independent samples, and then the obtained results are extended to dependent data. In each case, the asymptotic distribution of the test statistic is stated under the null hypothesis as well as under alternatives, which allows to study the consistency of the test. Specifically, it is shown that the test statistic is asymptotically free distributed under the null hypothesis. The finite sample performance of the test is studied via simulation. A real data set application is included.

Suggested Citation

  • M. D. Jiménez-Gamero & J. de Uña-Álvarez, 2024. "Testing Poissonity of a large number of populations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(1), pages 81-105, March.
    • Handle: RePEc:spr:testjl:v:33:y:2024:i:1:d:10.1007_s11749-023-00883-w
    DOI: 10.1007/s11749-023-00883-w
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    References listed on IDEAS

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