On the computation of the exact distribution of power divergence test statistics

Marco A. Marhuenda; Yolanda Marhuenda; Domingo Morales

Kybernetika (2003)

  • Volume: 39, Issue: 1, page [55]-74
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Marhuenda, Marco A., Marhuenda, Yolanda, and Morales, Domingo. "On the computation of the exact distribution of power divergence test statistics." Kybernetika 39.1 (2003): [55]-74. <http://eudml.org/doc/33622>.

@article{Marhuenda2003,
abstract = {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.},
author = {Marhuenda, Marco A., Marhuenda, Yolanda, Morales, Domingo},
journal = {Kybernetika},
keywords = {multinomial distribution; algorithms; goodness-of-fit divergence tests; power divergence statistics; chi-squared tests; power comparisons; multinomial distribution; goodness-of-fit divergence test; power divergence statistics; -squared test; power comparison},
language = {eng},
number = {1},
pages = {[55]-74},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On the computation of the exact distribution of power divergence test statistics},
url = {http://eudml.org/doc/33622},
volume = {39},
year = {2003},
}

TY - JOUR
AU - Marhuenda, Marco A.
AU - Marhuenda, Yolanda
AU - Morales, Domingo
TI - On the computation of the exact distribution of power divergence test statistics
JO - Kybernetika
PY - 2003
PB - Institute of Information Theory and Automation AS CR
VL - 39
IS - 1
SP - [55]
EP - 74
AB - 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.
LA - eng
KW - multinomial distribution; algorithms; goodness-of-fit divergence tests; power divergence statistics; chi-squared tests; power comparisons; multinomial distribution; goodness-of-fit divergence test; power divergence statistics; -squared test; power comparison
UR - http://eudml.org/doc/33622
ER -

References

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  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 (1966) MR0196777
  3. Cressie N. A. C., Read T. R. C., Multinomial goodness of fit tests, J. Roy. Statist. Soc. Ser. B 46 (1984), 440–464 (1984) Zbl0571.62017MR0790631
  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 (1963) MR0164374
  5. Kulmann H., Notes on the computation of the exact distribution function of the χ 2 and related tests statistics in the equiprobable case, Comput. Stat. Data Anal., The Statistical Software Newsletter 4 (1996), 707–710 (1996) 
  6. Liese F., Vajda I., Convex Statistical Distances, Teubner, Leipzig 1987 Zbl0656.62004MR0926905
  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 Zbl0663.62065MR0955054
  9. Weiss M. A., Data Structures and Algorithm Analysis, Benjamin/Cummings Publishing Company, Redwood City, CA 1992 Zbl0879.68016
  10. Zografos K., Ferentinos, K., Papaioannou T., 10.1080/03610929008830290, Comm. Statist. A – Theory Methods 19 (1990), 1785–1802 (1990) MR1075502DOI10.1080/03610929008830290

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