Abstract
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 Renyi entropies and order statistics. For the first time, we obtain the generating function of the Frechet 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. AMS Subject Classification Primary 60E05; secondary 62N05; 62F10
Highlights
The art of proposing generalized classes of distributions has attracted theoretical and applied statisticians due to their flexible properties
The last decade is full on new classes of distributions that become precious for applied statisticians
We propose a new class of distributions called the odd generalized exponential (“OGE” for short) family, which is flexible because of the hazard rate shapes: increasing, decreasing, J, reversed-J, bathtub and upsidedown bathtub
Summary
Muhammad H Tahir1*†, Gauss M Cordeiro2†, Morad Alizadeh3†, Muhammad Mansoor4†, Muhammad Zubair4† and Gholamhossein G Hamedani5†. The Islamia University of Bahawalpur, 63100 Bahawalpur, Pakistan Full list of author information is available at the end of the article
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