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December, 1947 Discriminating Between Binomial Distributions
Paul G. Hoel
Ann. Math. Statist. 18(4): 556-564 (December, 1947). DOI: 10.1214/aoms/1177730346


Given a set of $k$ random samples, $x_1, x_2, \cdots, x_k$, from a binomial distribution with parameters $p$ and $n$, it is shown that the familiar binomial index of dispersion $z = \frac{\sum^k_1 (x_i - \bar x)^2}{\bar x\big(1 - \frac{\bar x}{n_0}\big)}$ yields an approximate best critical region independent of $p$ for testing the hypothesis $n = n_0$ against the alternative hypothesis $n > n_0$, provided $\bar x$ and $n_0 - \bar x$ are not small. Because of the nature of the test, its optimum properties also apply to testing whether the data came from a binomial population with $n = n_0$ or from a Poisson population.


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Paul G. Hoel. "Discriminating Between Binomial Distributions." Ann. Math. Statist. 18 (4) 556 - 564, December, 1947.


Published: December, 1947
First available in Project Euclid: 28 April 2007

zbMATH: 0029.30803
MathSciNet: MR23035
Digital Object Identifier: 10.1214/aoms/1177730346

Rights: Copyright © 1947 Institute of Mathematical Statistics

Vol.18 • No. 4 • December, 1947
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