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Symmetric Bernoulli Distributions and Generalized Binomial Distributions
Author(s) -
Qu Y.,
Greene T.,
Piedmonte M. R.
Publication year - 1993
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710350503
Subject(s) - mathematics , binomial distribution , beta binomial distribution , continuity correction , negative binomial distribution , binomial (polynomial) , bernoulli's principle , statistics , beta negative binomial distribution , latent variable , multinomial distribution , quasi likelihood , latent variable model , binomial proportion confidence interval , engineering , poisson distribution , aerospace engineering
The generalized binomial distribution is defined as the distribution of a sum of symmetrically distributed Bernoulli random variates. Several two‐parameter families of generalized binomial distributions have received attention in the literature, including the Polya urn model, the correlated binomial model and the latent variable model. Some properties and limitations of the three distributions are described. An algorithm for maximum likelihood estimation for two‐parameter generalized binomial distributions is proposed. The Polya urn model and the latent variable model were found to provide good fits to sub‐binomial data given by Parkes. An extension of the latent variable model to incorporate heterogeneous response probabilities is discussed.