The beta odd log-logistic generalized family of distributions

Abstract

We introduce a new family of continuous models called thelog-logistic generalized familymathematical properties.of distributions.beta oddWe study some of itsIts density function can be symmetrical,left-skewed, right-skewed, reversed-J, unimodal and bimodal shaped,and has constant, increasing, decreasing, upside-down bathtub andJ-shaped hazard rates.Five special models are discussed.We ob-tain explicit expressions for the moments, quantile function, momentgenerating function, mean deviations, order statistics, Rényi entropyand Shannon entropy. We discuss simulation issues, estimation by themethod of maximum likelihood, and the method of minimum spacingdistance estimator. We illustrate the importance of the family by meansof two applications to real data sets.