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Teor. Veroyatnost. i Primenen., 1965, Volume 10, Issue 3, Pages 488–499 (Mi tvp544)  

On a characterization of the Poisson distribution and its statistical applications

L. N. Bol'shev

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: The distributions of $n$ mutually independent random variables $X_1,…,X_n$ are Poisson ones if and only if the conditional joint distribution of $X_1,…,X_n$ given $\Sigma X_i=K$ is the multinomial distribution (4). If we wish to test the hypothesis that $X_1,…,X_n$ are Poisson random variables we can use the conditional test (8). This test considered as an unconditional one is asymptotically the most powerful test against close binomial or negative binomial alternatives. The characterization of the Poisson distribution and its extensions for the binomial and the negative binomial distributions can be used to generate Poisson, binomial or negative binomial random numbers.

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English version:
Theory of Probability and its Applications, 1965, 10:3, 446–456

Bibliographic databases:

Received: 16.03.1965

Citation: L. N. Bol'shev, “On a characterization of the Poisson distribution and its statistical applications”, Teor. Veroyatnost. i Primenen., 10:3 (1965), 488–499; Theory Probab. Appl., 10:3 (1965), 446–456

Citation in format AMSBIB
\Bibitem{Bol65}
\by L.~N.~Bol'shev
\paper On a~characterization of the Poisson distribution and its statistical applications
\jour Teor. Veroyatnost. i Primenen.
\yr 1965
\vol 10
\issue 3
\pages 488--499
\mathnet{http://mi.mathnet.ru/tvp544}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=208728}
\zmath{https://zbmath.org/?q=an:0202.50201}
\transl
\jour Theory Probab. Appl.
\yr 1965
\vol 10
\issue 3
\pages 446--456
\crossref{https://doi.org/10.1137/1110052}


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