|
Teoriya Veroyatnostei i ee Primeneniya, 1965, Volume 10, Issue 3, Pages 488–499
(Mi tvp544)
|
|
|
|
This article is cited in 20 scientific papers (total in 20 papers)
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 $X_1,\dots,X_n$ are Poisson ones if and only if the conditional joint distribution of $X_1,\dots,X_n$ given $\Sigma X_i=K$ is the multinomial distribution (4). If we wish to test the hypothesis that $X_1,\dots,X_n$ 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.
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
Linking options:
https://www.mathnet.ru/eng/tvp544 https://www.mathnet.ru/eng/tvp/v10/i3/p488
|
Statistics & downloads: |
Abstract page: | 488 | Full-text PDF : | 490 | First page: | 1 |
|