Abstract:
We present several recursive procedures for calculating exact (non-limit) distributions of decomposable statistics in the multinomial scheme. In order to obtain recurrence relations, we make use of the generating functions of the statistics under consideration. In the general case, the method of calculating reduces to the algorithm suggested by A. Zubkov in 1996 which is presented in the language of Markov chains.
Citation:
B. I. Selivanov, “On calculation of exact distributions of decomposable statistics in the multinomial scheme”, Diskr. Mat., 18:3 (2006), 85–94; Discrete Math. Appl., 16:4 (2006), 359–369
\Bibitem{Sel06}
\by B.~I.~Selivanov
\paper On calculation of exact distributions of decomposable statistics in the multinomial scheme
\jour Diskr. Mat.
\yr 2006
\vol 18
\issue 3
\pages 85--94
\mathnet{http://mi.mathnet.ru/dm61}
\crossref{https://doi.org/10.4213/dm61}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2289323}
\zmath{https://zbmath.org/?q=an:1126.60012}
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\transl
\jour Discrete Math. Appl.
\yr 2006
\vol 16
\issue 4
\pages 359--369
\crossref{https://doi.org/10.1515/156939206778609714}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33846870617}
Linking options:
https://www.mathnet.ru/eng/dm61
https://doi.org/10.4213/dm61
https://www.mathnet.ru/eng/dm/v18/i3/p85
This publication is cited in the following 2 articles:
A. M. Zubkov, M. V. Filina, “Computation of distributions of statistics by means of Markov chains”, Discrete Math. Appl., 32:4 (2022), 285–295
Marina Filina, Andrey Zubkov, “Algorithm of exact computation of decomposable statistics distributions and its applications”, Lecture Notes in Comput. Sci., 10684 (2017), 476–484
Citation in format AMSBIB
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