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An expectation-maximization algorithm for estimating the parameters of the correlated binomial distribution

The correlated binomial (CB) distribution was proposed by Luceño (Computational Statistics $\&$ Data Analysis, 20, 1995, 511-520) as an alternative to the binomial distribution for the analysis of the data in the presence of correlations among events. Due to the complexity of the mixture likelihood of the model, it may be impossible to derive analytical expressions of the maximum likelihood estimators (MLEs) of the unknown parameters. To overcome this difficulty, we develop an expectation-maximization algorithm for computing the MLEs of the CB parameters. Numerical results from simulation studies and a real-data application showed that the proposed method is very effective by consistently reaching a global maximum. Finally, our results should be of interest to senior undergraduate or first-year graduate students and their lecturers with an emphasis on the interested applications of the EM algorithm for finding the MLEs of the parameters in discrete mixture models.