The beta odd log-logistic generalized family of distributions

Abstract

We introduce a new family of continuous models called the log-logistic generalized family mathematical properties. of distributions. beta odd We study some of its Its density function can be symmetrical, left-skewed, right-skewed, reversed-J, unimodal and bimodal shaped, and has constant, increasing, decreasing, upside-down bathtub and J-shaped hazard rates. Five special models are discussed. We ob- tain explicit expressions for the moments, quantile function, moment generating function, mean deviations, order statistics, Rényi entropy and Shannon entropy. We discuss simulation issues, estimation by the method of maximum likelihood, and the method of minimum spacing distance estimator. We illustrate the importance of the family by means of two applications to real data sets.