The Kumaraswamy Gumbel distribution |
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Authors: | Gauss M Cordeiro Saralees Nadarajah Edwin M M Ortega |
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Institution: | (1) Department of Statistics, Chonnam National University, Gwangju, 500-757, South Korea;(2) College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, OR, USA |
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Abstract: | The Gumbel distribution is perhaps the most widely applied statistical distribution for problems in engineering. We propose
a generalization—referred to as the Kumaraswamy Gumbel distribution—and provide a comprehensive treatment of its structural
properties. We obtain the analytical shapes of the density and hazard rate functions. We calculate explicit expressions for
the moments and generating function. The variation of the skewness and kurtosis measures is examined and the asymptotic distribution
of the extreme values is investigated. Explicit expressions are also derived for the moments of order statistics. The methods
of maximum likelihood and parametric bootstrap and a Bayesian procedure are proposed for estimating the model parameters.
We obtain the expected information matrix. An application of the new model to a real dataset illustrates the potentiality
of the proposed model. Two bivariate generalizations of the model are proposed. |
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