A new compounded four-parameter lifetime model: Properties, cure rate model and applications

We propose a new four-parameter lifetime distribution obtained by compounding twouseful distributions: the Weibull and Burr XII distributions. Among interesting features,it shows a great flexibility with respect to its crucial functions shapes; the probability density function can exhibit unimodal (symmetrical and right-skewed), bimodal and decreasing shapes, and the hazard rate function can accommodate increasing, decreasing, bathtub, upside-down bathtub and decreasing-increasing-decreasing shapes. Some mathematicalproperties of the new distribution are obtained such as the quantiles, moments, generatingfunction, stress-strength reliability parameter and stochastic ordering. The maximum likelihood estimation is employed to estimate the model parameters. A Monte Carlo simulationstudy is carried out to assess the performance of the maximum likelihood estimates. Wealso propose a flexible cure rate survival model by assuming that the number of competingcauses of the event of interest has the Poisson distribution and the time for the event followsthe proposed distribution. Four empirical illustrations of the new distribution are presentedto real-life data sets. The results of the proposed model are better in comparison to thoseobtained with the exponential-Weibull, odd Weibull-Burr and Weibull-Lindley models