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Abstract
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We propose a new family of continuous distributions called the odd generalized
exponential family, whose hazard rate could be increasing, decreasing, J, reversed-J,
bathtub and upside-down bathtub. It includes as a special case the widely known
exponentiated-Weibull distribution. We present and discuss three special models in the
family. Its density function can be expressed as a mixture of exponentiated densities
based on the same baseline distribution. We derive explicit expressions for the ordinary
and incomplete moments, quantile and generating functions, Bonferroni and Lorenz
curves, Shannon and Rényi entropies and order statistics. For the first time, we obtain
the generating function of the Fréchet distribution. Two useful characterizations of the
family are also proposed. The parameters of the new family are estimated by the
method of maximum likelihood. Its usefulness is illustrated by means of two real
lifetime data sets
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