Marhuenda, Marco A.; Marhuenda, Yolanda; Morales, Domingo On the computation of the exact distribution of power divergence test statistics. (English) Zbl 1249.60070 Kybernetika 39, No. 1, 55-74 (2003). Summary: We introduce several algorithms to generate the vectors in the support of a multinomial distribution. Computational studies are carried out to analyze their efficiency with respect to CPU time and to calculate their efficiency bounds. The proposed algorithm is used to calculate exact distributions of the power divergence test statistics under the hypothesis of uniformity. Finally, several exact power comparisons are carried out for different divergence statistics and families of alternatives to the uniformity hypothesis. Cited in 1 Document MSC: 60G10 Stationary stochastic processes 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) Keywords:multinomial distribution; goodness-of-fit divergence test; power divergence statistics; \(\chi \)-squared test; power comparison PDF BibTeX XML Cite \textit{M. A. Marhuenda} et al., Kybernetika 39, No. 1, 55--74 (2003; Zbl 1249.60070) Full Text: Link EuDML References: [1] Aho A. V., Hopcroft J. E., Ullman J. D.: Data Structures and Algorithms. Addison-Wesley, Massachusetts 1983 · Zbl 0487.68005 [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 · Zbl 0203.19902 [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 [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 · Zbl 0124.08703 [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 [6] Liese F., Vajda I.: Convex Statistical Distances. Teubner, Leipzig 1987 · Zbl 0656.62004 [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 [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 [9] Weiss M. A.: Data Structures and Algorithm Analysis. Benjamin/Cummings Publishing Company, Redwood City, CA 1992 · Zbl 0879.68016 [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 · Zbl 0724.62007 · doi:10.1080/03610929008830290 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.