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Teor. Veroyatnost. i Primenen., 1965, Volume 10, Issue 3, Pages 479–487 (Mi tvp543)  

This article is cited in 1 scientific paper (total in 1 paper)

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 $\mathscr P$.

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English version:
Theory of Probability and its Applications, 1965, 10:3, 438–445

Bibliographic databases:

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

Citation in format AMSBIB
\Bibitem{Pro65}
\by Yu.~V.~Prokhorov
\paper On a~characterisation of a~class of probability distributions by those of some statistics
\jour Teor. Veroyatnost. i Primenen.
\yr 1965
\vol 10
\issue 3
\pages 479--487
\mathnet{http://mi.mathnet.ru/tvp543}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=211440}
\zmath{https://zbmath.org/?q=an:0202.50202}
\transl
\jour Theory Probab. Appl.
\yr 1965
\vol 10
\issue 3
\pages 438--445
\crossref{https://doi.org/10.1137/1110051}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. V. Belomestny, A. V. Prokhorov, “Stability of characterization the independence of random variables by the independence of the linear statistics”, Theory Probab. Appl., 59:4 (2015), 672–677  mathnet  crossref  crossref  mathscinet  isi  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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