The beta power distribution. (English) Zbl 1230.60011

Summary: The power distribution is defined as the inverse of the Pareto distribution. We study in full detail a distribution the so-called beta power distribution. We obtain analytical forms for its probability density and hazard rate functions. Explicit expressions are derived for moments, probability weighted moments, the moment generating function, mean deviations, Bonferroni and Lorenz curves, moments of order statistics, entropy and reliability. We estimate the parameters by the maximum likelihood method. The practicability of the model is illustrated in two applications to real data.


60E05 Probability distributions: general theory
62E10 Characterization and structure theory of statistical distributions


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