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Teoriya Veroyatnostei i ee Primeneniya, 1965, Volume 10, Issue 3, Pages 479–487
(Mi tvp543)
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This article is cited in 17 scientific papers (total in 17 papers)
On a characterisation of a class of probability distributions by those of some statistics
Yu. V. Prokhorov V. A. Steklov Mathematical Institute, USSR Academy of Sciences
Abstract:
Let $\mathscr P$ be a class of probability distributions of random element $X$. The question is whether there exist a statistic $Y=f(X)$ possesing two following properties: 1$^\circ$. Its distribution $Q_P^Y$ under $P\in\mathscr P$ does not depend on $P$, $Q_P^Y=Q_\mathscr P^Y$. 2$^\circ$. If for some $P'$ $Q_{P'}^Y=Q_\mathscr P^Y$ then $P'\in\mathscr P$. The question is solved positively for some special families $\mathscr P$.
Received: 21.05.1965
Citation:
Yu. V. Prokhorov, “On a characterisation of a class of probability distributions by those of some statistics”, Teor. Veroyatnost. i Primenen., 10:3 (1965), 479–487; Theory Probab. Appl., 10:3 (1965), 438–445
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Abstract page: | 285 | Full-text PDF : | 97 | First page: | 2 |
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