Generalization of Log-Logistic Family with Quantile Regression Model

A new general class of distributions is proposed by applying the transformation to the random variable that follows the generalized odd-logistic family. Using the proposed family, we introduce a flexible Weibull distribution. The importance of the proposed distribution is demonstrated and compared with different generalizations of the Weibull distribution via three real data applications. A quantile regression model is obtained using the newly developed Weibull model and compared with the standard Weibull quantile regression model through a real data application.