On the Computation of the Maximum Likelihood Estimates of the Parameters in a Mixture Model
Keywords:Poisson distribution, singular distribution, mixture distribution, maximum likelihood estimation, conditional maximum likelihood estimation, EM algorithm
AbstractA social group may consist of sterile and fertile couples where sterile couples cannot reproduce. When the number of children for a fertile couple is distributed according to a Poisson distribution, the probability distribution of the number of children per couple in the social group is a mixture of a distribution singular at zero and a Poisson distribution. The estimation of the parameters in the mixture distribution is considered in this paper. Since the maximum likelihood (ML) metod does not provide estimates in closed forms, it is proposed to obtain the estimates using the EM algorithm. A stepwise procedure for computing the estimates is presented. A stepwise procedure for computing the estimates is presented. A numerical study is carried out to compare these estimates with the conditional ML estimates determined using Newton-Raphson iterative procedure.