An Extension of the Weibull Distribution via Alpha Logarithmic G Family with Associated Quantile Regression Modeling and Applications

In this paper, a novel lifetime model based on the Weibull distribution is presented. The new model is named the alpha logarithmic Weibull. The alpha logarithmic Weibull distribution has a decreasing, increasing and monotone hazard rate. Some distributional properties of the new model including the hazard rate function, moments, order statistics, and stochastic ordering are obtained. The new model includes some special sub-models and they are reported in detail. We examined five estimation methods which are maximum likelihood, Anderson-Darling, Cramer-von Mises least-squares and weighted least squares, to estimate three parameters of the new distribution. Extensive simulation studies are also conducted to observe the performance of the five estimators. Based on the new distribution, a new quantile regression model is also introduced. To estimate the parameters of a novel quantile regression model, the maximum likelihood technique is examined. Two practical examples are studied to show the capacity of the new lifetime and quantile regression models.