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The validation of a beta-binomial model for overdispersed binomial data. (English) Zbl 1362.62045

Summary: The beta-binomial model has been widely used as an analytically tractable alternative that captures the overdispersion of an intra-correlated, binomial random variable, \(X\). However, the model validation for \(X\) has been rarely investigated. As a beta-binomial mass function takes on a few different shapes, the model validation is examined for each of the classified shapes in this article. Further, the mean square error (MSE) is illustrated for each shape by the maximum likelihood estimator (MLE) based on a beta-binomial model approach and the method of moments estimator (MME) in order to gauge when and how much the MLE is biased.

MSC:

62F10 Point estimation
62P10 Applications of statistics to biology and medical sciences; meta analysis

References:

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