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