Direct calculation of maximum likelihood estimator for the bivariate Poisson distribution (Q1058242)

To estimate the parameter vector \(\lambda\) of the bivariate Poisson distribution we would like to calculate the maximum likelihood estimator (MLE) \({\hat \lambda}\). This MLE \({\hat \lambda}\) has not a simple expression as \(\bar X,\) \(S^ 2,..\). etc. We only have information about MLE \({\hat \lambda}\) by normal equations and its variation forms. \textit{P. Holgate} [Biometrika 51, 241-245 (1964; Zbl 0133.118)] shows the asymptotic property of MLE \({\hat \lambda}\). In this paper we present a calculating method of MLE \({\hat \lambda}\). The method is constructed by direct calculation of likelihood function and by a searching routine of MLE \({\hat \lambda}\) which maximizes the function value. A sequence of random numbers coming from a bivariate Poisson distribution P(\(\lambda)\) is given. The change of the value of the likelihood function varying parameter \(\lambda\) in our rule is calculated and the performance of the searching routine is discussed in detail. In the last part of this paper a numerical interpretation of our routine is shown.