A New Family of Additive Weibull-Generated Distributions

Abstract

The additive Weibull distribution is an extended version of the most widely used Weibull distribution which is a quite flexible model for analyzing lifetime data. In this paper, a new family of distributions called additive Weibull generated (AW-G) is defined and studied.The new family includes the Weibull-G family which was previously worked out by Bourguignon et al. [7]. Four sub-models are introduced and studied in some details. Explicit expressions for the ordinary moments, quantile, order statistics and reliability are obtained. The method of maximum likelihood is used to estimate the model parameters of the family. The additive Weibull-G family may serve as a viable alternative to other distributions for modeling data arising in various fields such as the physical and biological sciences, survival analysis and engineering. The importance of the additive Weibull-G family is concluded by means of two real data sets.