Generalized binomial distributions
- 1 January 1993
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics - Theory and Methods
- Vol. 22 (11) , 3065-3086
- https://doi.org/10.1080/03610929308831203
Abstract
In many cases where the binomial dismbution fails to apply to real world data it is because of more variability in the data than can be explained by that dismbution. Several authors have proposed models that are useful in explaining extra-binomial variation. In this paper we point out a characterization of sequences of exchangeable Bernoulli random variables which can be used to develop models which show more variability than the binomial. We give sufficient conditions which will yield such models and show how existig models can be combined to generate further models. The usefulness of some of these models is illustrated by fitting them to sets of real data.Keywords
This publication has 16 references indexed in Scilit:
- A Markov chain model of extrabinomial variationBiometrika, 1990
- A new class of modified binomial distributions with applications to certain toxicological experiments∗Communications in Statistics - Theory and Methods, 1989
- Estimating multiple rater agreement for a rare diagnosisJournal of Multivariate Analysis, 1988
- Modelling the Extraneous Variance in the Presence of Extra-Binomial VariationJournal of the Royal Statistical Society Series C: Applied Statistics, 1987
- On the beta-correlated binomial (bcb) distribution - a three parameter generalization of the binomial distributionCommunications in Statistics - Theory and Methods, 1987
- Binary Regression Using an Extended Beta-Binomial Distribution, With Discussion of Correlation Induced by Covariate Measurement ErrorsJournal of the American Statistical Association, 1986
- A three-parameter generalization of the binomial distributionCommunications in Statistics - Theory and Methods, 1985
- Gaussian Estimation for Correlated Binomial DataJournal of the Royal Statistical Society Series B: Statistical Methodology, 1985
- Two Generalizations of the Binomial DistributionJournal of the Royal Statistical Society Series C: Applied Statistics, 1978
- A Probability Distribution Derived from the Binomial Distribution by Regarding the Probability of Success as Variable between the Sets of TrialsJournal of the Royal Statistical Society Series B: Statistical Methodology, 1948