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.
Kiefer, J. and Wolfowitz, J. (1956). Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters. Ann. Math. Statist., 4, 887–906.
van der Vaart, A.W. (1998). Asymptotic statistics. Cambridge University Press, New York.
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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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