Improved point estimation for the Kumaraswamy distribution
We develop nearly unbiased estimators for the Kumaraswamy distribution proposed by Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J. Hydrol. 46 (1980), pp. 79-88], which has considerable attention in hydrology and related areas. We derive modified maximum-likelihood estimators that are bias-free to second order. As an alternative to the analytically bias-corrected estimators discussed, we consider a bias correction mechanism based on the parametric bootstrap. We conduct Monte Carlo simulations in order to investigate the performance of the corrected estimators. The numerical results show that the bias correction scheme yields nearly unbiased estimates.
kumaraswamy distribution maximum-likelihood estimation bias correction bootstrap beta distribution