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The asymptotic distribution of a likelihood ratio test statistic for the homogeneity of poisson distribution

Abstract

Brown and Zhao (2012) (Sankhyā, Series A, Volume 64, pp 611–625) developed a new test for the Poisson distribution and compared it with the likelihood ratio test (LRT) and some other tests. They claimed that under the null hypothesis, the asymptotic distribution of the LRT statistic was \(\chi_{n-1}^{2}\). In this paper we derive the asymptotic distribution of the LRT statistic reported in Brown and Zhao (2012). Our results show that Brown and Zhao’s claim is wrong. We discuss the reason for their mistake.

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References

  • Brown, L.D. and Zhao, L.H. (2012). A test for the Poisson distribution. Sankhyā, Series A, 64, 611–625.

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Acknowledgement

This research was supported by grants 5U19AI056390-05 and 3 UL1 RR024160-02S1 from the National Institutes of Health. Comments from attendants in a seminar at the University of Rochester Department of Biostatistics are greatly appreciated.

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Correspondence to Changyong Feng.

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Feng, C., Wang, H. & Tu, X.M. The asymptotic distribution of a likelihood ratio test statistic for the homogeneity of poisson distribution. Sankhya A 74, 263–268 (2012). https://doi.org/10.1007/s13171-012-0003-y

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  • DOI: https://doi.org/10.1007/s13171-012-0003-y

Keywords and phrases.

  • Poisson distribution
  • delta-method
  • asymptotic equivalence

AMS (2000) subject classification.

  • Primary 62E20
  • Secondary 62F03
  • 62F12