The Flexible Weibull Extension-Burr XII Distribution: Model, Properties and Applications

Abstract

This paper is devoted to study a new four- parameter additive model. The newly suggested model is referred to as the flexible Weibull extension-Burr XII distribution. It is derived by considering a serial system with one component following a flexible Weibull extension distribution and another following a Burr XII distribution. The usefulness of the model stems from the flexibility of its failure rate which accommodates bathtub and modified bathtub among other risk patterns. These two patterns have been widely accepted in several fields, especially reliability and engineering fields. In addition, the importance of the new distribution is that it includes new sub-models which are not known in the literature. Some statistical properties of the proposed distribution such as quantile function, the mode, the rth moment, the moment generating function and the order statistics are discussed. Moreover, the method of maximum likelihood is used to estimate the parameters of the model. Also, to evaluate the performance of the estimators, a simulation study is carried out. Finally, the performance of the proposed distribution is compared through a real data set to some well-known distributions including the new modified Weibull, the additive Burr and the additive Weibull distributions. It is shown that the proposed model provides the best fit for the used real data set.

Multi-component Reliability Inference in Modified Weibull Extension Distribution and Progressive Censoring Scheme

“…For example, a new five parameter distribution, known as the modified beta flexible Weibull extension distribution, is derived and studied by Abubakari et al [ 1 ]. Kamal and Ismail [ 12 ] considered the flexible Weibull Extension-Burr XII distribution. Nassar et al [ 19 ] introduced a new extension of Weibull distribution, called Alpha logarithmic transformed Weibull distribution that provides better fits than some of its known generalizations.…”

The Additive Flexible Weibull Extension-Lomax Distribution: Properties and Estimation with Applications to COVID-19 Data

“…Osagie and Osemwenkhae (2020) constructed the Lomax-Weibull (L-W) distribution. Kamal and Ismail (2020) presented the flexible Weibull extension-Burr XII distribution by combining the flexible Weibull extension distribution (FWE) obtained by Bebbington et al (2007a) and Burr XII distribution in a series system. Thach and Bris (2021) introduced the additive Chen-Weibull distribution.…”

Bayesian Estimation of a Transmuted Topp-Leone Length Biased Exponential Model Based on Competing Risk with the Application of Electrical Appliances

“…Many authors looked at the burr extensions model as: [13][14][15], etc. Many authors looked at the burr family of statistical models as: [16], etc.…”