Kamps (1995a,b) has introduced generalized order statistics as random variables having certain joint density function which includes as a special case the joint density functions of many models of ordered random variables. Let F be an absolutely continuous distribution function with density function f The random variables X 1 n m̃ k X n n m̃ k are called generalized order statistics based on F if...

A Bernstein-type exponential inequality for (generalized) canonical U -statistics of order 2 is obtained and the Rosenthal and Hoffmann-Jørgensen inequalities for sums of independent random variables are extended to (generalized) U -statistics of any order whose kernels are either nonnegative or canonical.

The Kumaraswamy distribution is similar to the Beta distribution but has the key advantage of a closed-form cumulative distribution function. In this paper we present the estimation of Kumaraswamy distribution parameters based on Generalized Order Statistics (GOS) using Maximum Likelihood Estimators (MLE). We proved that the parameters estimation for Kumaraswamy distribution can not be obtained...