Closed form expressions for moments of the beta Weibull distribution

Abstract

The beta Weibull distribution was first introduced by Famoye et al. (2005) and studied by these authors and Lee et al. (2007). However, they do not give explicit expressions for the moments. In this article, we derive explicit closed form expressions for the moments of this distribution, which generalize results available in the literature for some sub-models. We also obtain expansions for the cumulative distribution function and Rényi entropy. Further, we discuss maximum likelihood estimation and provide formulae for the elements of the expected information matrix. We also demonstrate the usefulness of this distribution on a real data set.

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“…is the density function of the beta Weibull (BW) distribution proposed by Cordeiro et al [19] with parameters a > 0, b > 0, λ > 0, and c > 0, where B(a, b)…”

“…For a random variable Y following the BW (a, b, λ, c) distribution, Cordeiro et al [19] showed that the mgf of Y , for real non-integer a > 0, is given by…”

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