Abstract: The Empirical Bayes (EB) test of parameters in Kumaraswamy distribution Family is investigated under linear loss function. By using the recursive kernel estimation and the monotone of Empirical Bayes function in case of iid samples, the EB test rules are constructed. Under suitable conditions the order of convergence rates approaches to O(n－λ(s－2.5)s－1), where s≥3， s∈N*.

Key words: Kumaraswamy distribution family, recursive kernel estimation, Bayes test, empirical Bayes function, convergence rates