A new family of generalized distributions

Abstract

Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J. Hydrol. 462 (1980), pp. 79–88] introduced a distribution for double-bounded random processes with hydrological applications. For the first time, based on this distribution, we describe a new family of generalized distributions (denoted with the prefix ‘Kw’) to extend the normal, Weibull, gamma, Gumbel, inverse Gaussian distributions, among several well-known distributions. Some special distributions in the new family such as the Kw-normal, Kw-Weibull, Kw-gamma, Kw-Gumbel and Kw-inverse Gaussian distribution are discussed. We express the ordinary moments of any Kw generalized distribution as linear functions of probability weighted moments (PWMs) of the parent distribution. We also obtain the ordinary moments of order statistics as functions of PWMs of the baseline distribution. We use the method of maximum likelihood to fit the distributions in the new class and illustrate the potentiality of the new model with an application to real data.

Keywords:

• gamma distribution
• Kumaraswamy distribution
• moments
• normal distribution
• order statistics
• Weibull distribution

AMS Subject Classification :

• 62E10
• 62F03
• 62F05
• 62F10

Acknowledgements

We would like to thank an anonymous referee for helpful comments and suggestions which improved the paper. The work of the first author is partially supported by CNPq, Brazil.