Research article of American Journal of Computer Sciences and Applications
On Transmuted Flexible Weibull Extension Distribution with Applications to Different Lifetime Data Sets
Ahmad1, Zawar Hussain2
Research Scholar: Department of Statistics, Quaid-i-Azam University 45320, Islamabad 44000, Pakistan1
Assistant Professor: Department of Statistics, Quaid-i-Azam University 45320, Islamabad 44000, Pakistan2
In this article, a three parameters transmuted version of the flexible Weibull extension distribution called transmuted flexible Weibull extension distribution is studied. The proposed model is very flexible and is able to model real phenomena with increasing, unimodal or modified unimodal failure rates. Explicit expressions for mathematical properties are derived. Maximum likelihood estimates and asymptotic confidence bounds for the unknown parameters of the model are also obtained. Four real data sets are analyzed in order to illustrate the flexibility of the proposed distribution.
Keywords:Flexible Weibull extension distribution, Modified unimodal failure rate, Order statistics, Moment generating function, Maximum likelihood estimation
How to cite this article:
Zubair Ahmad and Zawar Hussain. On Transmuted Flexible Weibull Extension Distribution with Applications to Different Lifetime Data Sets. American Journal of Computer Sciences and Applications, 2017; 1:1 DOI: 10.28933/ajcsa-2017-05-1801
 Ahmad, Z. and Iqbal, B. (2017). Generalized Flexible Weibull Extension Distribution. Circulation in Computer, Volume 2(4), 68-75. https:/doi.org/10.22632/css-252-11.
 Attardi. L., Guida, M. and Pulcini, G. (2005). A mixed-Weibull regression model for the analysis of automotive warranty data. Reliab Eng & Syst Saf; 87:265–73.
 Aryal, G.R., and Tsokos, C.P. (2011). Transmuted Weibull Distribution. European journal of pure and applied mathematics, Vol. 4, No. 2, 89-102.
 Ashour, S. K. and Eltehiwy, M. A. (2013). Transmuted exponentiated modified Weibull distribution. International Journal of Basic and Applied Science 2 (3) 258-269.
 Bebbington, M., Lai, C. D. and Zitikis, R. (2007). A flexible Weibull extension. Reliability Engineering and System Safety, 92, 719-726.
 Durham, S. D. and Padgett, W. J. (1997). Cumulative damage model for system failure with application to carbon fibers and composites. Technometrics; 39:34–44.
 Elbatal. I. and Aryal, G. (2013). On the Transmuted Additive Weibull Distribution. AUSTRIAN JOURNAL OF STATISTICS. Volume 42. Number 2, 117–132
 El-Gohary, A., El-Bassiouny, A. H., and El-Morshedy, M. (2015). Inverse Flexible Weibull Extension Distribution.
 Hanook, S., Shahbaz, M. Q., Mohsin, M. and Golam Kibria, B. M. (2013). A note on beta inverse Weibull distribution. Communications in Statistics-Theory and Methods, 42, 320-335.
 Khan, M. S., and King, R. (2013). Transmuted modified Weibull distribution. European Journal Of Pure And Applied Mathematics, Vol. 6, No. 1, 66-88.
 Khan, A. H. and Jan, T.R. (2016). The new modified generalized linear failure rate distribution. J. Stat. Appl. Pro. Lett. 3, No. 2, 83-95
 Merovci, F., Elbatal. I. and Ahmed, A. (2014), The transmuted generalized inverse Weibull distribution. Austrian Journal of Statistics. Volume 43/2, 119–131.
 Nadarajah, S, and Kotz, S.(2005). On the recent papers on modiﬁed Weibull distributions. IEEE Trans Reliab ;54:61-2.
 Nicholas, M. D. and Padgett, W. J. (2006). A bootstrap control chart for Weibull percentiles, Quality and Reliability Engineering International, 22, 141-151.
 Nofal, Z. M., Afify, A. Z., Yousof, H. M., Granzotto. D.C.T. and Louzada, F. (2016). Kumaraswamy transmuted exponentiated Additive Weibull distribution. International Journal of Statistics and Probability; Vol. 5, No. 2.
 Stacy, E. W. (1962). A generalization of the gamma distribution. The Annals of Mathematical Statistics, 33(3), 1187-1192.
 Shaw, W. T., and Buckley, I. R. (2009). The alchemy of probability distributions: beyond Gram-Charlier expansions and a skew-kurtotic-normal distribution from a rank transmutation map. ArXiv preprint, arXiv: 0901.0434.
 Silva, G. O., Ortega, E. M. and Cordeiro, G. M. (2010). The beta modified Weibull distribution. Lifetime data analysis, 16(3), 409-430.
 Tahir, M. H., Cordeiro, G. M., Mansoor, M. and Zubair, M. (2015). The Weibull-Lomax Distribution: Properties and Applications’, Hacettepe Journal of Mathematics and Statistics.
 Xie, M. and Lai, C. D. (1996). Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function. Reliability Engineering and System Safety, 52(1), 87-93.
 Zajicek, G. (2011). A new kind of medical cancer epidemiology. Available at: http://www.what-is-cancer.com/papers/newmedicine/epidemiologyFrame.htm.