  The correlated binomial (CB) distribution was proposed by Luce\~no
(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.
