Improved point estimation for the Kumaraswamy distribution

Abstract

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.

Keywords:

• beta distribution
• bias correction
• bootstrap
• Kumaraswamy distribution
• maximum-likelihood estimation

Acknowledgements

The financial support from Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP/Brazil) is gratefully acknowledged. The author thanks an anonymous referee for the comments and suggestions that led to a much improved paper.