A new family of generalized distributions

• Published in: Journal of statistical computation and simulation Vol. 81; no. 7; pp. 883 - 898
• Main Authors: Cordeiro, Gauss M., de Castro, Mário
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 01-07-2011; Taylor & Francis Ltd
• Subjects: Computer simulation; gamma distribution; Inverse; Kumaraswamy distribution; Mathematical analysis; Mathematical models; Maximum likelihood method; moments; Normal distribution; order statistics; Parents; Probability distribution; Random processes; Statistics; Weibull distribution
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949650903530745

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.