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 [,1]m, in a class of discrete distributions, including Binomial(,),kθ Negative Binomial(,),rθ discrete Weibull()θ and etc., is considered. We give necessary and sufficient conditions for which the Bayes estimator of ,θ 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 m for which the corresponding Bayes estimator of θ is minimax