A bivariate truncated Poisson distribution in terms of Gram Charlier polynomials is defined.A lower truncation in both variables at any points X s 1 X s 2 ,is considered. The probability function of the distribution is expressed in terms of univariate Poisson distribution functions. The probabilities of the bivariate Poisson distribution for given correlation coefficient are tabulated for ρ=0.25,0.5,0.75. Using the cannonical form of the distribution rsth factorial moments of the distribution are obtained. The method of moments is used to find the estimates of the parameters of the marginals λ1,λ2 and the correlation coefficient ρ. The asymtotic variances of these estimates are considered. An example is given to illustrate the application of the estimators and their variances.
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