A new family of generalized distributions

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 gener...

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Vydané v:Journal of statistical computation and simulation Ročník 81; číslo 7; s. 883 - 898
Hlavní autori: Cordeiro, Gauss M., de Castro, Mário
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Abingdon Taylor & Francis 01.07.2011
Taylor & Francis Ltd
Predmet:
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
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Shrnutí: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.
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ISSN:0094-9655
1563-5163
DOI:10.1080/00949650903530745