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

Arslan Nasir (1) , Farrukh Jamal (2) , Akbar Ali Sha (1)

1 IUB - The Islamia University of Bahawalpur
2 Sadiq Abbas Post Graduate College

We propose a new four-parameter lifetime distribution by compounding the Weibull and Burr XII models so-called the minimum Weibull-Burr (minWB) distribution, which is quite flexible with respect to the density and hazard rate shapes. The density can exhibit uni-modal (symmetrical and right-skewed), bimodal and decreasing shapes, and the hazard rate 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 quantile function, 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 minWB distribution. Four empirical illustrations of the new distribution are presented to real-life data sets and the results of the proposed model are better as compared to those of the exponential-Weibull, odd Weibull-Burr and Weibull-Lindley models.

Mots clés: Burr distribution; compounding; cure rate model; hazard rate; lifetime distri-bution; maximum likelihood method; Poisson distribution; Weibull distribution

Domaines: Statistiques [stat]

Arslan Nasir, Farrukh Jamal, Akbar Ali Sha. A new compounded four-parameter lifetime model: Properties, cure rate model and applications. 2018. ⟨hal-01902847v1⟩