Article Code : 13971026166945

Article Title : The Exponentiated Odd Log-Logistic Family of Distributions‎: ‎Properties and Applications

Keywords : tre

Journal Number : 2 Spring-Summer 2018

Visited : 27

Files : 1.02 MB

List of Authors

  Full Name Email Grade Degree Corresponding Author
1 Morad Alizadeh Assistant Professor PhD
2 Saeid Tahmasebi Associate Professor PhD
3 Hossein Haghbin Assistant Professor PhD


Based on the generalized log-logistic family (\cite {Gleaton:Lynch:2006}) 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 (\cite {Gleaton:Lynch:2006}) 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 R\'{e}nyi 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.