Complete sufficiency and maximum likelihood estimation for the two- parameter negative binomial distribution
type: Item
instance of: scholarly article
title: Complete sufficiency and maximum likelihood estimation for the two- parameter negative binomial distribution
zbMATH Open document ID: 0602.62021
DOI: 10.1007/BF01894768
author: L. J. Willson
author: J. Leroy Folks
author: John H. Young
published in: Metrika
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/176079
review text: The estimation problem of both parameters in the two-parameter negative binomial distribution is discussed in the finite sample case. It is shown that the minimal sufficient statistic is not complete, and that the maximum likelihood estimator (mle) for the shape parameter k exists if the sample variance is strictly larger than the sample mean. Contours and 3-dimensional plots of the log-likelihood function indicate that the mle for k is highly non-robust.
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 62B05
zbMATH DE Number: 3971972
zbMATH Keywords: completeness
zbMATH Keywords: order statistic
zbMATH Keywords: two-parameter negative binomial distribution
zbMATH Keywords: minimal sufficient statistic
zbMATH Keywords: maximum likelihood estimator
zbMATH Keywords: shape parameter
zbMATH Keywords: sample variance
zbMATH Keywords: sample mean
zbMATH Keywords: Contours
MaRDI profile type: Publication
cites work: SAMPLING THEORY OF THE NEGATIVE BINOMIAL AND LOGARITHMIC SERIES DISTRIBUTIONS
cites work: Q4043971
cites work: Q5802576
OpenAlex ID: W2001768421
description: scientific article; zbMATH DE number 3971972