The Burr XII modified Weibull distribution: model, properties and applications

A new distribution called Burr XII modified Weibull (BXIIMW or BMW) distribution is presented and its properties explored. This new distribution contains several new and well known sub-models, including Burr-Weibull, Burr-exponential, Burr-Rayleigh, Burr XII, Lomax modified Weibull, Lomax-Weibull, Lomax-exponential, Lomax-Rayleigh, Lomax, Weibull, Rayleigh, and exponential distributions. Some structural properties of the proposed distribution including the shapes of the density and hazard rate functions, moments, conditional moments, moment generating function, skewness and kurtosis are presented. Mean deviations, Lorenz and Bonferroni curves, R\'enyi entropy and the distribution of the order statistics are given. The maximum likelihood estimation technique is used to estimate model parameters and finally applications of the model to real data sets are presented to illustrate the usefulness of the proposed distribution.