The problem of testing hypotheses concerning the parameters of the Pólya distribution
type: Item
instance of: scholarly article
title: The problem of testing hypotheses concerning the parameters of the Pólya distribution
zbMATH Open document ID: 0906.62011
DOI: 10.1007/BF02365363
author: S. V. Kameneva
author: Ya. P. Lumel'skii
published in: Journal of Mathematical Sciences (New York)
publication date: 1998-11-24T00:00:00Z
review text: The Pólya distribution has the following form: \[ {\mathbf P}_{p,\lambda} (\xi =x/n) ={n\choose x} {p^{[x;\lambda]} (1-p)^{[n-x; \lambda]} \over 1^{[n; \lambda]}}; \tag{1} \] here \(a^{[r;\gamma]} =\prod^{r-1}_{h=0} (a+\gamma h)\) and \(a^{[0; \gamma]}=1\); \(\lambda\) satisfies the condition \(\min\{p+ n\lambda; 1-p+n \lambda\} >0\) (for \(\lambda\geq 0\) this condition is always fulfilled). When \(\lambda=0\), distribution (1) reduces to the binomial law. For \(\lambda= -1/N\); \(p=M/N\) with \(M,N\) being some natural numbers and \(0<M<N\), distribution (1) reduces to the hypergeometric law. The problem of testing hypotheses concerning the parameter \(p\) of the binomial distribution is classical. This problem is a particular case of the problem of testing hypotheses concerning the parameter \(p\) of the Pólya distribution with the parameter \(\lambda\) assumed known. There are a few papers devoted to distinguishing the binomial and hypergeometric distributions. This problem, as well as many others, is also a particular case of a more general problem of testing hypotheses concerning the value of the parameter \(\lambda\) of the Pólya distribution. We solve the problems of testing hypotheses concerning the parameters \(p\) and \(\lambda\) of the Pólya distribution. Numerical examples are also considered.
Mathematics Subject Classification ID: 62F03
zbMATH DE Number: 1213174
zbMATH Keywords: Pólya distribution
zbMATH Keywords: hypergeometric law
zbMATH Keywords: binomial distribution
MaRDI profile type: Publication
cites work: Q3262608
cites work: Q5561562
cites work: Q5801671
cites work: Discrimination between the binomial and hypergeometric models
cites work: Q5600597
full work available at URL: https://doi.org/10.1007/bf02365363
OpenAlex ID: W2065373534
description: scientific article; zbMATH DE number 1213174