# Article

 Title: On the computation of the exact distribution of power divergence test statistics (English) Author: Marhuenda, Marco A. Author: Marhuenda, Yolanda Author: Morales, Domingo Language: English Journal: Kybernetika ISSN: 0023-5954 Volume: 39 Issue: 1 Year: 2003 Pages: [55]-74 Summary lang: English . Category: math . Summary: In this paper we introduce several algorithms to generate all the vectors in the support of a multinomial distribution. Computational studies are carried out to analyze their efficiency with respect to the CPU time and to calculate their efficiency frontiers. The proposed algorithm is used to calculate exact distributions of power divergence test statistics under the hypothesis of uniformity. Finally, several exact power comparisons are done for different divergence statistics and families of alternatives to the uniformity hypothesis. (English) Keyword: multinomial distribution Keyword: algorithms Keyword: goodness-of-fit divergence tests Keyword: power divergence statistics Keyword: chi-squared tests Keyword: power comparisons MSC: 60G10 MSC: 62G10 MSC: 62M10 MSC: 62Q05 idZBL: Zbl 1249.60070 idMR: MR1980124 . Date available: 2009-09-24T19:51:09Z Last updated: 2015-03-23 Stable URL: http://hdl.handle.net/10338.dmlcz/135508 . Reference: [1] Aho A. V., Hopcroft J. E., Ullman J. D.: Data Structures and Algorithms.Addison–Wesley, Massachusetts 1983 Zbl 0487.68005, MR 0666695 Reference: [2] Ali S. M., Silvey S. D.: A general class of coefficient of divergence of one distribution from another.J. Roy. Statist. Soc. Ser. B 286 (1966), 131–142 MR 0196777 Reference: [3] Cressie N. A. C., Read T. R. C.: Multinomial goodness of fit tests.J. Roy. Statist. Soc. Ser. B 46 (1984), 440–464 Zbl 0571.62017, MR 0790631 Reference: [4] Csiszár I.: Eine Informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizität von Markoffschen Ketten.Publ. Math. Inst. Hungarian Academy of Sciences, Series A, 8 (1963), 85–108 MR 0164374 Reference: [5] Kulmann H.: Notes on the computation of the exact distribution function of the $\chi ^2$ and related tests statistics in the equiprobable case.Comput. Stat. Data Anal., The Statistical Software Newsletter 4 (1996), 707–710 Reference: [6] Liese F., Vajda I.: Convex Statistical Distances.Teubner, Leipzig 1987 Zbl 0656.62004, MR 0926905 Reference: [7] Marhuenda M. A., Marhuenda, Y., Morales D.: Algorithms to calculate the exact distribution function of power divergence statistics.Technical Report of the Operational Research Center, Miguel Hernández University of Elche 2001 Reference: [8] Read T. R. C., Cressie N. A. C.: Goodness–of–fit Statistics for Discrete Multivariate Data.Springer–Verlag, New York 1988 Zbl 0663.62065, MR 0955054 Reference: [9] Weiss M. A.: Data Structures and Algorithm Analysis.Benjamin/Cummings Publishing Company, Redwood City, CA 1992 Zbl 0879.68016 Reference: [10] Zografos K., Ferentinos, K., Papaioannou T.: $\phi$-divergence statistics: sampling properties, multinomial goodness of fit and divergence tests.Comm. Statist. A – Theory Methods 19 (1990), 1785–1802 MR 1075502, 10.1080/03610929008830290 .

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