The exponentiated odd log-logistic family of distributions: properties and applications

Based on the generalized log-logistic family (Gleaton and Lynch (۲۰۰۶)) of distributions, we propose a new family of continuous distributions with two extra shape parameters called the exponentiated odd log-logistic family. It extends the class of exponentiated distributions, odd log-logistic family (Gleaton and Lynch (۲۰۰۶)) and any continuous distribution by adding two shape parameters. Some special cases of this family are discussed. We investigate the shapes of the density and hazard rate functions. The proposed family has also tractable properties such as various explicit expressions for the ordinary and incomplete moments, quantile and generating functions, probability weighted moments, Bonferroni and Lorenz curves, Shannon and Rényi entropies, extreme values and order statistics, which hold for any baseline model. The model parameters are estimated by maximum likelihood and the usefulness of the new family is illustrated by means of three real data sets.

Keywords:

Generated family , Maximum likelihood , Moment , Odd log-logistic distribution , Probability weighted moment , Quantile function , Rényi entropy