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The Kumaraswamy Weibull distribution with application to failure data. (English) Zbl 1202.62018
Summary: We introduce and study some mathematical properties of the P. Kumaraswamy [J. Hydrol. 46, 79–88 (1980)] Weibull distribution that is a quite flexible model in analyzing positive data. It contains as special sub-models the exponentiated Weibull, exponentiated Rayleigh, exponentiated exponential, Weibull and also the new Kumaraswamy exponential distribution. We provide explicit expressions for the moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, reliability and Rényi entropy. The moments of the order statistics are calculated. We also discuss the estimation of the parameters by maximum likelihood. We obtain the expected information matrix. We provide applications involving two real data sets on failure times. Finally, some multivariate generalizations of the Kumaraswamy Weibull distribution are discussed.

62E10 Characterization and structure theory of statistical distributions
62E20 Asymptotic distribution theory in statistics
62N05 Reliability and life testing
62E15 Exact distribution theory in statistics
62F10 Point estimation
62N02 Estimation in survival analysis and censored data
Full Text: DOI
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