A Versatile Family of Generalized Log-logistic Distributions: Unimodality, Bimodality, Regression, and Applications

Abstract

In real-world applications, it is not uncommon to encounter situations in which a set of data exhibits asymmetry and bimodality. Because of this, this paper proposes a new versatile family of generalized log-logistic distributions using the method of T-R{Y} framework. The resulting flexible classes of this family includes both unimodal and bimodal distributions which can be expected to model a wide variety of data with different levels of skewness. The distributional and structural properties of the classes are discussed. The method of maximum likelihood is used for estimating the distributions parameters and a simulation study is conducted to examine its performance. The usefulness and goodness-of-fit of some members of these classes are illustrated by means of six real data sets. The strength of these members is shown consistently by giving better fits than some of the competitors with the same number of parameters. In addition, a new generalized log-logistic lifetime regression model is introduced and applied to fit a right-censored data with covariates. The flexibility provided by this model could be very helpful in describing and explaining different types of lifetime data.