The Empirical Bayes Estimation For The Parameter Of The Gamma Distribution Families In The Case Of NA Samples

For the independent and identical distribution samples,the results of empirical Bayes estimator are mostly considered in the literature. However random samples are often not independent and identically distributed in reliability theory, infiltration theory and multivariate statistical analysis. Gamma distribution families are often applied in survival data analysis, so it is very significant to estimate its shape parameter. Huang Jiangping shows the convergence rates of EB estimation of the parameter of the standard Gamma distribution families. In a more common situation, this paper discusses the Bayes estimation problem for the shape parameter of the Gamma distribution families under the square error loss. And the empirical Bayes(EB) estimator is constructed by using the identically distributed and negatively associated(NA) samples. Furthermore the convergence rate of the EB estimator is obtained under suitable conditions. It has more universalities and practicalities compared to Huang Jiangping's article.