Comparative Study between Partial Bayes and Empirical Bayes Method in Gamma Distribution

Abstract

Though the name Partial Bayes was used earlier in a different context, but in statistics this is started from 2021, (Banerjee and Seal, 2021). Also, we know that empirical Bayes method was studied extensively for several decades. In this paper, these two methods are compared in two parameter gamma distribution having shape and scale parameter. As expected, it is found that empirical Bayes method is good in some cases. However, partial Bayes method performs even better in some cases where the shape parameter is sufficiently small, i.e. variation in the data is small. Even, overall performances of these two methods do not differ too much. But whenever we have information that shape parameter is small, then in that case partial Bayes method performs well. These results are also found by extensive simulation technique. The performances of these two estimators are also compared using two real datasets.