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Teoriya Veroyatnostei i ee Primeneniya, 1967, Volume 12, Issue 2, Pages 307–321 (Mi tvp707)  

This article is cited in 13 scientific papers (total in 13 papers)

Necessary and Sufficient Statistics for the Family of Shifts of Probability Distributions on Continious Bicompact Groups

V. M. Maksimov

Moscow
Abstract: It is shown that if the family of probability distributions $p_y(x)=p(xy)$ on a bicompact group $G$, where $x\in G$ and $y\in G$, has nontrivial sufficient statistics for the parameter $у$ then the density $p(x)$ may be written in the form $p(x)=\exp\Bigl(\lambda+\sum_{k=1}^sc_k\varphi_k(x)\Bigr)$ where $1,\varphi_1(x),\dots,\varphi_s(x)$ is a basis of the set of entries of the matrix $\{g_{ij}(x)\}$ of a certain real finite-dimensional representation of group $G$.
The case when $p(x)$ may be equal to zero is also considered (here we deal mainly with the case when $G$ is the circle group).
Received: 14.01.1966
English version:
Theory of Probability and its Applications, 1967, Volume 12, Issue 2, Pages 267–280
DOI: https://doi.org/10.1137/1112029
Bibliographic databases:
Language: Russian
Citation: V. M. Maksimov, “Necessary and Sufficient Statistics for the Family of Shifts of Probability Distributions on Continious Bicompact Groups”, Teor. Veroyatnost. i Primenen., 12:2 (1967), 307–321; Theory Probab. Appl., 12:2 (1967), 267–280
Citation in format AMSBIB
\Bibitem{Mak67}
\by V.~M.~Maksimov
\paper Necessary and Sufficient Statistics for the Family of Shifts of Probability Distributions on Continious Bicompact Groups
\jour Teor. Veroyatnost. i Primenen.
\yr 1967
\vol 12
\issue 2
\pages 307--321
\mathnet{http://mi.mathnet.ru/tvp707}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=214175}
\zmath{https://zbmath.org/?q=an:0174.50302}
\transl
\jour Theory Probab. Appl.
\yr 1967
\vol 12
\issue 2
\pages 267--280
\crossref{https://doi.org/10.1137/1112029}
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  • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
     
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