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PARAMETER ESTIMATION AND APPLICATIONS FOR A GENERALISATION OF THE BETA‐BINOMIAL DISTRIBUTION
Author(s) -
Danaher P.J.
Publication year - 1988
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1988.tb00621.x
Subject(s) - beta binomial distribution , beta negative binomial distribution , binomial distribution , mathematics , beta distribution , binomial (polynomial) , negative binomial distribution , statistics , bayes' theorem , binomial proportion confidence interval , multinomial distribution , distribution (mathematics) , maximum likelihood , continuity correction , econometrics , bayesian probability , poisson distribution , mathematical analysis
Summary A three‐parameter generalisation of the beta‐binomial distribution (BBD) derived by Chandon (1976) is examined. We obtain the maximum likelihood estimates of the parameters and give the elements of the information matrix. To exhibit the applicability of the generalised distribution we show how it gives an improved fit over the BBD for magazine exposure and consumer purchasing data. Finally we derive an empirical Bayes estimate of a binomial proportion based on the generalised beta distribution used in this study.