Integer-parameter estimation in discrete distributions

Integer-parameter restriction quite often occurs naturally in real life situations. Here we consider the problem of deriving the maximum likelihood estimators (MLE) for the case in which the parameter is restricted to a positive integer. The usual asymptotic theory for the MLE does not hold good any more and each case needs individual attention for the derivation of these results,. The estimation problem in the case of Poisson, Binomial, and Poisson-Binomial bivariate model is investigated here, A simple method of deriving the MLE and the lower bound for the variance of the integer-parameter estimator is also discussed