Compound Multinomial Likelihood Functions are Unimodal: Proof of a Conjecture of I. J. Good

Levin, Bruce; Reeds, James

Ann. Statist., Tome 5 (1977) no. 1, p. 79-87 / Harvested from Project Euclid

Résumé

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.

Publié le : 1977-01-14
Classification: Maximum likelihood estimate, unimodality, multinomial distribution, Dirichlet distribution, negative binomial distribution, variation-diminishing, Laplace transform, 62F10, 62F15, 44A10, 44A35

@article{1176343741,
     author = {Levin, Bruce and Reeds, James},
     title = {Compound Multinomial Likelihood Functions are Unimodal: Proof of a Conjecture of I. J. Good},
     journal = {Ann. Statist.},
     volume = {5},
     number = {1},
     year = {1977},
     pages = { 79-87},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176343741}
}

Levin, Bruce; Reeds, James. Compound Multinomial Likelihood Functions are Unimodal: Proof of a Conjecture of I. J. Good. Ann. Statist., Tome 5 (1977) no. 1, pp.  79-87. http://gdmltest.u-ga.fr/item/1176343741/