A new compounded four-parameter lifetime model: Properties, cure rate model and applications
Résumé
We propose a new four-parameter lifetime distribution obtained by compounding two
useful 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 mathematical
properties of the new distribution are obtained such as the quantiles, moments, generating
function, stress-strength reliability parameter and stochastic ordering. The maximum likelihood estimation is employed to estimate the model parameters. A Monte Carlo simulation
study is carried out to assess the performance of the maximum likelihood estimates. We
also propose a flexible cure rate survival model by assuming that the number of competing
causes of the event of interest has the Poisson distribution and the time for the event follows
the proposed distribution. Four empirical illustrations of the new distribution are presented
to real-life data sets. The results of the proposed model are better in comparison to those
obtained with the exponential-Weibull, odd Weibull-Burr and Weibull-Lindley models.
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