The properties of Topp Leone exponentiated weibull distribution with application to survival data
Author Affiliations
- 1Faculty of Physical Sciences, Department of Statistics, Ahmadu Bello University, Zaria, Nigeria
Res. J. Mathematical & Statistical Sci., Volume 9, Issue (1), Pages 9-15, January,12 (2021)
Abstract
In this study, a new four-parameter lifetime distribution called the Topp Leone exponentiated Weibull distribution was introduced. The model includes several important sub-models as special cases such as Topp Leone Weibull, exponentiated Weibull and Weibull distributions. A linear representation for the probability distribution function was carried out. Some mathematical properties of the distribution were presented such as moments, moment generating function, quantile function, survival function, hazard function, reversed hazard function and odd function. The distribution of order statistic was obtained. Estimation of the parameters by maximum likelihood method was discussed. Two real-life application of the distribution was presented and the analysis showed the fit and flexibility of the new distribution over some lifetime models considered. The analysis showed that the model is effective in fitting survival data.
References
- Silva, G. O., Ortega, E. M. M. and Cordeiro, G. M. (2010). The beta modified Weibull distribution, Lifetime Data Analysis, 16(3), 409-430., undefined, undefined
- Cordeiro, G. M., Ortega, E. M. M. and Nadarajah, S. (2010). The KumaraswamyWeibull distribution with application to failure data, Journal of Franklin Institute, 347: 1399-1429., undefined, undefined
- Aryal, G. R. and Tsokos, C. P. (2011).Transmuted Weibull distribution: a generalization of the Weibull probability distribution, European Journal of Pure and Applied Mathematics, 4: 89-102., undefined, undefined
- Shahbaz, M. Q., Shahbaz, S. and Butt, N. M. (2012).The Kumaraswamy inverse Weibull distribution. Pakistan Journal of Statistics Operation Research, 8, 3: 479-489., undefined, undefined
- Cordeiro, G. M., Ortega, E. M. M. and Da Cunha, D. C. C. (2013). The exponentiated generalized class of distributions, Journal of Data Science, 11: 1-27., undefined, undefined
- Merovci, F. andElbatal, I. (2013). The McDonald modified Weibull distribution: properties and applications. arXiv preprint arXiv:13092961.2013 (In Press)., undefined, undefined
- Hanook, S., Shahbaz, M. Q., Mohsin, M. and Kibria, G. (2013). A Note on Beta Inverse Weibull Distribution. Communication in Statistics: Theory and Methods, 42: 320-335., undefined, undefined
- Elbatal, I. and Aryal, G. (2013).On the transmuted additive Weibull distribution. Austrian Journal of Statistics, 42: 117-132., undefined, undefined
- Codeiro, G. M., Hashimot, E. M. and Ortega, E. M. (2014).The McDonald Weibull model.Statistics: A Journal of Theoretical and Applied Statistics, 48(2): 256-278., undefined, undefined
- Cordeiro, G. M., Ortega, E. M. M. and Silva, G. O. (2014). The Kumaraswamy modified Weibull distribution: theory and applications, Journal of Statistical Computation Simulation, 84: 1387-1411., undefined, undefined
- Afify, A. Z., Nofal, Z. M. and Butt, N. S. (2014).Transmuted complementary Weibull geometric distribution.Pakistan Journal of Statistics and Operation Research, 10: 435-454., undefined, undefined
- 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, 5: 78-99., undefined, undefined
- Nofal, Z. M., Afify, A. Z., Yousof, H. M. and Cordeiro, G. M. (2017).The generalized transmuted-G family of distributions. Communication in Statistics: Theory and Methods, 46: 4119-4136., undefined, undefined
- Aryal, G. R., Ortega, E. M. M., Hamedani, G. G. and Yousof, H. M. (2017). The Topp-Leone generated Weibull distribution: regression model, characterizations and applications. International Journal of Statistics and Probability, 6: 126-141., undefined, undefined
- Afify, A. Z., Cordeiro, G. M., Butt, N. S., Ortega, E. M. M. and Suzuki, A. K. (2017).A new lifetime model with variable shapes for the hazard rate.Brazilian Journal of Probability and Statistics, 31: 516-541., undefined, undefined
- Afify, A. Z., Cordeiro, G. M., Yousof, H. M., Abdus, S. and Ortega, E. M. M. (2018). The Marshall-Olkin additive Weibull distribution with variable shapes for the hazard rate, Hacettepe Journal of Mathematics and Statistics, 47: 365-381., undefined, undefined
- Ibrahim, S., Doguwa, S. I., Audu, I. and Jibril, H. M. (2020). On the Topp Leone exponentiated-G Family of Distributions: Properties and Applications, Asian Journal of Probability and Statistics, 7(1): 1-15., undefined, undefined
- Feigl, P. and Zelen, M. (1965).Estimation of exponential probabilities with concomitant information.Biometrics, 21:826-38., undefined, undefined
- Aarset, M. V. (1987).How to identify a bathtub hazard rate. IEEE Transactions on Reliability, 36(1): 106-8., undefined, undefined