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On the Marshall–Olkin extended Weibull distribution

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Abstract

We study some mathematical properties of the Marshall–Olkin extended Weibull distribution introduced by Marshall and Olkin (Biometrika 84:641–652, 1997). We provide explicit expressions for the moments, generating and quantile functions, mean deviations, Bonferroni and Lorenz curves, reliability and Rényi entropy. We determine the moments of the order statistics. We also discuss the estimation of the model parameters by maximum likelihood and obtain the observed information matrix. We provide an application to real data which illustrates the usefulness of the model.

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Authors and Affiliations

  1. Departamento de Estatística, Universidade Federal de Pernambuco, Recife, PE, Brazil

    Gauss M. Cordeiro

  2. Departamento de Estatística, Universidade de São Paulo, São Paulo, SP, Brazil

    Artur J. Lemonte

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  1. Gauss M. Cordeiro
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  2. Artur J. Lemonte
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Correspondence to Artur J. Lemonte.

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Cordeiro, G.M., Lemonte, A.J. On the Marshall–Olkin extended Weibull distribution. Stat Papers 54, 333–353 (2013). https://doi.org/10.1007/s00362-012-0431-8

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  • DOI: https://doi.org/10.1007/s00362-012-0431-8

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