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

Abstract : 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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https://hal.archives-ouvertes.fr/hal-01902847
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Submitted on : Friday, March 8, 2019 - 7:35:04 AM
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  • HAL Id : hal-01902847, version 2

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Arslan Nasir, Farrukh Jamal, Christophe Chesneau, Akbar Shah. A new compounded four-parameter lifetime model: Properties, cure rate model and applications. 2019. ⟨hal-01902847v2⟩

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