A comparison of homogeneity tests in Poisson distribution based on Mont Carlo simulation

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Abstract. In this article, we introduce tests for examining the hypothesis of whether the observations in a Poisson distribution with the same parameters fit with the observations of Poisson distribution with different parameters. When Poisson parameter is small, and the sample volume is large, homogeneity tests like Conditional Chi-square test, Likelihood ratio, and Nymen-Scott test are not efficient enough. Therefore, in this article, another test which is efficient enough in these conditioned is introduced, named Anscombe test. At last, based on Mont Carlo simulation we compare these tests in terms of performance and accuracy, and we illustrate use of them through a real example.


homogeneity test, likelihood ratio test, chi-square test, Anscombe transformation, Poisson distribution

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Parsian, A. (2009). Mathematical statistics (2nd edition), Isfahan Industrial University Publications.

Anscombe F.J. (1948). The transformation of Poisson, binomial and negativebinomial data, Biometrika.35, 246-254.

Bartlett, M.S. (1947). The use of transformations, Biometrics, 3, 39-52.

Brown, L.D. and Zhao, L.H.(2002). A test for the Poisson disterbution,Sankhya: 64, Series A, Pt.3,611-625.

Cochran, W.G. (1954). Some method of string thing the common 2χTest, Biometrics, 10, 417-4

Brown, L.D., Zhang, R. and Zhao L.(2001). Root un-root methodologhy for non- parametric density estimation and Poisson random effects models. Technical report. www.stat.wharton.upenn.edu/1brown.

Mood, A.M., Graybill, F.A.andBoes, D, C..(1997). "Introduction to the Theory of Statistic" 3 ED., Mc. Graw-Hill Book Company, New York.

Rice, J. (1995). Mathematical Statistic and Data Analysis. Second edition. Duxbury press, CA.