Open Access
Translator Disclaimer
January, 1977 Compound Multinomial Likelihood Functions are Unimodal: Proof of a Conjecture of I. J. Good
Bruce Levin, James Reeds
Ann. Statist. 5(1): 79-87 (January, 1977). DOI: 10.1214/aos/1176343741

Abstract

I. J. Good's 1965 conjecture of the unimodality of the likelihood function of a symmetrical compound multinomial distribution is proved by the variation-diminishing property of the Laplace transform. The result is a special case of a several sample version with asymmetrical compounding Dirichlet distributions. The technique of proof is applied to yield similar results for the negative binomial distribution and a two point mixture of Poissons.

Citation

Download Citation

Bruce Levin. James Reeds. "Compound Multinomial Likelihood Functions are Unimodal: Proof of a Conjecture of I. J. Good." Ann. Statist. 5 (1) 79 - 87, January, 1977. https://doi.org/10.1214/aos/1176343741

Information

Published: January, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0382.62028
MathSciNet: MR451503
Digital Object Identifier: 10.1214/aos/1176343741

Subjects:
Primary: 62F10
Secondary: 44A10 , 44A35 , 62F15

Keywords: Dirichlet distribution , Laplace transform , maximum likelihood estimate , multinomial distribution , negative binomial distribution , Unimodality , variation-diminishing

Rights: Copyright © 1977 Institute of Mathematical Statistics

JOURNAL ARTICLE
9 PAGES


SHARE
Vol.5 • No. 1 • January, 1977
Back to Top