Cumulative hypergeometric processes: A statistical role for the \(_ nF_{n-1}\) functions
type: Item
instance of: scholarly article
title: Cumulative hypergeometric processes: A statistical role for the \(_ nF_{n-1}\) functions
zbMATH Open document ID: 0671.60006
DOI: 10.1016/0022-247X(88)90176-X
author: Mizan Rahman
author: Michael R. Hoare
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: The authors look at the problem of sampling without replacement leading to a generalization of the classical discrete hypergeometric probability model. The dependence of the probability of success from trial to trial is assumed to be governed by a certain recurrence relation. The distribution function for the number of successes is derived and it is shown that this can be written in terms of a hypergeometric function of the type \({}_ pF_{p-1}\). Several particular situations and limiting cases leading to generalized binomials and negative binomials are also considered.
Mathematics Subject Classification ID: 60C05
Mathematics Subject Classification ID: 33E15
zbMATH DE Number: 4098378
zbMATH Keywords: sampling without replacement
zbMATH Keywords: hypergeometric probability model
zbMATH Keywords: hypergeometric function
zbMATH Keywords: generalized binomials and negative binomials
reviewed by: Arakaparampil M. Mathai
MaRDI profile type: Publication
cites work: Cumulative Bernoulli trials and Krawtchouk processes
cites work: Q5556830
cites work: Q5508372
full work available at URL: 0022-247x(88)90176-x
OpenAlex ID: W2049270806
description: scientific article; zbMATH DE number 4098378