Ml estimation in the bivariate poisson distribution in the presence of missing values via the em algorithm

Abstract

In this paper we study the maximum likelihood estimation of parameters, of the bivariate Poisson distribution, by assuming a sample with a general pattern of missing observations and applying the EM algorithm (Dempster, Laird and Rubin, 1977). The application of the method is outlined in the complete-data estimation problem, considered by Holgate (1964), since the latter can be viewed as a special case of the missing-value problem studied here. The observed information matrix is also obtained by means of the EM algorithm (Louis, 1982) and numerical examples are presented. The application of Louis's method is found most appropriate and seen to produce remarkable acceleration in the convergence of the EM algorithm. Results of some interest, concerning the conditional distributions of Poisson variables given particular sums of Poisson random variables are also established.

Keywords:

• Bivariate Poisson distribution
• Conditional distributions
• EM algorithm
• Missing values