Statistical Estimation Based on Generalized Order Statistics from Kumaraswamy Distribution

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 in explicit forms, and therefore it has been implemented using the simulated data for illustrative purposes. We compare the performances of parameters estimation through an extensive numerical simulation for different sample sizes. These simulations examine the sensitivity of estimation to different sample sizes. In particular, how do estimations perform for small, moderate and large sample sizes? The main findings are: First, the worst performance estimation for small sample size selection for different values of the parameters estimation. Secondly, as the sample size increases the MSE of the estimation decreases. Finally, the estimation accuracy reaches its superiority for large sample sizes.