Minimax Estimator of a Lower Bounded Parameter of a Discrete Distribution under a Squared Log Error Loss Function

The problem of estimating the parameter θ, when it is restricted to an interval of the form, in a class of discrete distributions, including Binomial Negative Binomial discrete Weibull and etc., is considered. We give necessary and sufficient conditions for which the Bayes estimator of with respect to a two points boundary supported prior is minimax under squared log error loss function. For some of the distributions in this class, we give numerical values of the smallest values of for which the corresponding Bayes estimator of is minimax.