The Burr X Exponentiated Weibull Model: Characterizations,Mathematical Properties and Applications to Failure and Survival Times Data

Abstract

In this article, we introduce a new three-parameter lifetime model called the Burr X exponentiated Weibull model. The major justification for the practicality of the new lifetime model is based on the wider use of the exponentiated Weibull and Weibull models. We are motivated to propose this new lifetime model because it exhibits increasing, decreasing, bathtub, J shaped and constant hazard rates. The new lifetime model can be viewed as a mixture of the exponentiated Weibull distribution. It can also be viewed as a suitable model for fitting the right skewed, symmetric, left skewed and unimodal data. We provide a comprehensive account of some of its statistical properties. Some useful characterization results are presented. The maximum likelihood method is used to estimate the model parameters. We prove empirically the importance and flexibility of the new model in modeling two types of lifetime data. The proposed model is a better fit than the Poisson Topp Leone-Weibull, the Marshall Olkin extended-Weibull, gamma-Weibull , Kumaraswamy-Weibull , Weibull-Fréchet, beta-Weibull, transmuted modified-Weibull, Kumaraswamy transmuted- Weibull, modified beta-Weibull, Mcdonald-Weibull and transmuted exponentiated generalized-Weibull models so it is a good alternative to these models in modeling aircraft windshield data as well as the new lifetime model is much better than the Weibull-Weibull, odd Weibull-Weibull, Weibull Log-Weibull, the gamma exponentiated-exponential and exponential exponential-geometric models so it is a good alternative to these models in modeling the survival times of Guinea pigs. We hope that the new distribution will attract wider applications in reliability, engineering and other areas of research.

The Three-parameters Marshall-Olkin Generalized Weibull Model with Properties and Different Applications to Real Data Sets

“…The data consist of 84 observations. This data is recently analyzed by (Khalil et al (2019) and Mansour et al (2010b, c). In Table 1 and Table 2, we compared the fits of the MOGW distribution with the Odd Lindley exp W (OLEW), Burr-X exp W (BrXEW) ( : TTT plot, P-P plot, EPHF, EHRF for failure times data.…”

“…The second real data set corresponds to the survival times (in days) of 72 guinea pigs infected with virulent tubercle bacilli (see Bjerkedal (1960)). This data is recently analyzed by (Khalil et al (2019) and Mansour et al (2010b, c). We shall compare the fits of the MOGW distribution with those of other competitive models, namely: Odd Lindley exponentiated W (OLEW), the Odd WW (OWW) (Bourguignon et al (2014)), the gamma exponentiated-exponential (GaE-E) (Ristic and Balakrishnan (2012)).…”

“…This data consists of 63 observations of the strengths of 1.5 cm glass fibers. This data is recently analyzed by (Khalil et al (2019) and Mansour et al (2010b, c). We shall compare the fits of the MOGW with the OLEW, EW, TW and OLLW.…”

“…6.2 Modeling cancer data This data set represents the remission times (in months) of a random sample of 128 bladder cancer patients as reported in Lee and Wang (2003). This data is recently analyzed by (Khalil et al (2019) and Mansour et al (2010b, c).We compare the fits of the MOGW distribution with other competitive models, namely: The TMW, MBW, transmuted additive W distribution (TAW) (Elbatal and Aryal, (2013)), exponentiated transmuted generalized Rayleigh (ETGR) (Afify et al (2015)), and the Weibull distributions with corresponding densities (for > 0 ). Based on the figures in Table 4 we conclude that the proposed MOGW lifetime model is much better than the W, TMW, MBW, TAW, ETG-R models with (statistic) = 0.0672and (statistic) = 0.4214. : TTT plot, P-P plot, EPHF, EHRF for remission data set.…”

A New Parametric Life Distribution with Modified Bagdonavičius–Nikulin Goodness-of-Fit Test for Censored Validation, Properties, Applications, and Different Estimation Methods

“…A state-of-the-art survey on the class of such distributions can be found in ([ 1 ]). Some extensions of the W distribution with more than two parameters are available in the literature, such as exponentiated W (Exp-W) ([ 2 , 3 ]), the additive W ([ 4 ]), the Marshall–Olkin extended W ([ 5 ]), the beta inverse W ([ 6 ]), transmuted exponentiated generatized W ([ 7 ]), Marshall–Olkin additive W ([ 8 ]), the Topp Leone generated W distribution ([ 9 ]), the exponentiated generalized W Poisson ([ 10 ]), Type I general exponential W ([ 11 ]), new four-parameter W ([ 12 ]), Burr XII W ([ 13 ]), Marshall–Olkin generalized W Poisson ([ 14 ]), odd Lindley W ([ 15 ]), Lindley W ([ 16 ]), W generalized W ([ 17 ]), new extended W ([ 18 ]), Type II general exponential W ([ 19 ]), Burr X exponentiated W ([ 20 ]), odd power Lindley W ([ 21 ]), odd Nadarajah-Haghighi W ([ 22 ]), and WW Poisson ([ 23 ]).…”