, Volume 74, Issue 2, pp 263-268

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

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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.