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Le problème d'Anscombe pour les lois binomiales négatives généralisées
Author(s) -
Kokonendji Calestin C.
Publication year - 1999
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315501
Subject(s) - mathematics , index (typography) , negative binomial distribution , binomial distribution , binomial (polynomial) , statistics , sample (material) , distribution (mathematics) , combinatorics , physics , mathematical analysis , computer science , thermodynamics , world wide web , poisson distribution
Consider a finite sample from a generalized negative‐binomial distribution where both (canonical and index) parameters are unknown. This note proves that both the maximum‐likelihood estimate and the moment estimate of the index parameter exist if and only if the sample variance is greater than the sample mean. This extends a result for the negative‐binomial distribution that had been conjectured by Anscombe (1950) and later shown by Levin and Reeds (1977).