The Zografos-Balakrishnan odd log-logistic family of distributions: Properties and Applications

We study some mathematical properties of a new generator of continuous distributions with two additional shape parameters called theZografos-Balakrishnan odd log-logistic family. We present some specialmodels and investigate the asymptotes and shapes. The density function of the new family can be expressed as a mixture of exponentiateddensities based on the same baseline distribution. We derive a powerseries for its quantile function. Explicit expressions for the ordinary andincomplete moments, quantile and generating functions, Shannon andRényi entropies and order statistics, which hold for any baseline model,are determined. We estimate the model parameters by maximum likelihood. Two real data sets are used to illustrate the potentiality of theproposed family