On the mixture of flexible Weibull extension and Burr XII distributions

Abstract

This paper is devoted to study a new mixture model. This newly suggested model is a mixture of flexible Weibull extension and Burr XII distributions. We study the characteristics of the proposed distribution that includes probability density function, cumulative distribution function, reliability function and ageing behaviour through the failure rate function. Some statistical properties of the proposed distribution such as quantile function, the mode, median, r-th moments, the moment generating function and the order statistics are discussed. Moreover, the method of maximum likelihood is proposed for estimating the model parameters and also the Fisher's information matrix is derived. Finally, the performance of the proposed distribution is compared with existing distributions using applications of two real data sets to show the flexibility and efficiency of the new model.