On Neyman's conjecture: A characterization of the multinomials
type: Item
instance of: scholarly article
title: On Neyman's conjecture: A characterization of the multinomials
zbMATH Open document ID: 0583.62040
DOI: 10.1016/0047-259X(85)90030-2
author: Bikas K. Sinha
author: Thomas M. Gerig
published in: Journal of Multivariate Analysis
publication date: 1985-01-01T00:00:00Z
review text: The paper settles a conjecture by \textit{J. Neyman} [Certain chance mechanisms involving discrete distributions. in G. P. Patil (ed.): Classical and contagious discrete distributions, Proc. Int. Sympos., McGill Univ., Montreal, Que., 1963, 4-14 (1965)] concerning a characterization of positive and negative multinomial distributions by a linear regression property of power series distributions. The authors prove by means of a counter-example that the conjecture does not hold true if certain conditions are not satisfied and they state and prove a theorem that can be thought of as the corrected version of the conjecture.
Mathematics Subject Classification ID: 62H05
Mathematics Subject Classification ID: 62E10
zbMATH DE Number: 3934225
zbMATH Keywords: Neyman's conjecture
zbMATH Keywords: multivariate power series distributions
zbMATH Keywords: characterization
zbMATH Keywords: positive and negative multinomial distributions
zbMATH Keywords: linear regression property of power series distributions
zbMATH Keywords: counter-example
Wikidata QID: Q123358188
reviewed by: Evdokia Xekalaki
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3934225