Maximum likelihood estimation of the parameters of the bivariate binomial distribution
M. A. Hamdan, M. O Nasro · Communication in Statistics- Theory and Methods · 1986
We consider the problem of maximum likelihood estimation of the parameters of the bxvariate binomial distribution, In the statistical literature, this problem is solved when the observed sample is available in the form of a 2x2 contingency table, that is, with all four cell fre quencies given,, The present paper provides a solution for this problem when only the marginal totals of the 2x2 table are observed, which is the natural set-up in a bivariate sampling situation.. Thus, based on a sample [(Xi,Yi:), i = 1, …, k] from a bivariate binomial population, we derive maximum likelihood (ML) estimators for the two marginal parameters p1,p2: and the covariance parameter p11: It. turns out that the ML estimators for P1: and P2: are expressed explicitly in terms of the sample values, whereas the ML estimator for p11: can only be obtained numerically by iterative methods Two nu merical illustrations are also presented