A new extended log-Weibull regression: Simulations and applications

Abstract

The induction of one or more parameter(s) in parent distributions opened new doors for flexible modeling in modern distribution theory. Among well-established generalized (G) classes for flexible modeling, the exponentiated-G, Marshall-Olkin-G and odd log-logistic-G families offer induction of one additional parameter while the beta-G and Kumaraswamy-G classes offer two extra shape parameters. The Marshall-Olkin-odd-loglogistic-G (MOOLL-G) family serves as an alternative to the beta-G and Kumaraswamy-G classes. A new motivation for the MOOLL-G family for competing risk scenarios, some useful properties, and parameter estimation are addressed. The new log-MOOLL-Weibull regression is useful for analysis of real life data. The accuracy of the estimates and the residuals is addressed via Monte Carlo simulations. The presented models outperform some other well-known models.

Keywords

• generalized family
• Marshall-Olkin method
• maximum likelihood
• regression model
• Weibull distribution

References

1. [1] M.V. Aarset, How to identify bathtub hazard rate, IEEE Trans. Rel. 36 (1), 106-108, 1987.
2. [2] M. Alizadeh, G. Ozel, E. Altun, M. Abdi and G.G. Hamedani, The odd log-logistic Marshall-Olkin Lindley model for lifetime data, J. Stat. Theory Appl. 16 (3), 382-400, 2017.
3. [3] W. Barreto-Souza, Lemonte, A.J. and G.M. Cordeiro, General results for the Marshall and Olkin’s family of distributions, An. Acad. Brasil. Ciˆenc. 85 (1), 3-21, 2013.
4. [4] G.M. Cordeiro, M. Alizadeh, G. Ozel, B. Hosseinl, E.M.M. Ortega and E. Altun The generalized odd log-logistic family of distributions: Properties, regression models and applications, J. Stat. Comput. Simul. 87 (5), 908-932, 2017.
5. [5] G.M. Cordeiro, E.M. Hashimoto and E.M.M. Ortega, The McDonald Weibull model, Statistics 48 (2), 256-278, 2012.
6. [6] G.M. Cordeiro, E.M.M. Ortega and S. Nadarajah, The Kumaraswamy Weibull distribution with application to failure data, J Franklin Inst 347 (8), 1399-1429, 2010.
7. [7] G.M. Cordeiro, E.M.M. Ortega and S. Nadarajah, General results for the beta Weibull distribution, J. Stat. Comput. Simul. 83 (6), 1082-1114, 2013.
8. [8] J.N. da Cruz, E.M.M. Ortega and G.M. Cordeiro, The log-odd log-logistic Weibull regression model: modelling, estimation, influence diagnostics and residual analysis, J. Stat. Comput. Simul. 86 (8), 1516-1538, 2016.

9. [9] F. de Mendiburu and M.F. de Mendiburu, Package “agricolae”, R package version: 1-2, 2020.
10. [10] J.U. Gleaton and J.D. Lynch, On the distribution of the breaking strain of a bundle of brittle elastic fibers, Adv. in Appl. Probab. 36 (1), 98-115, 2004.
11. [11] J.U. Gleaton and J.D. Lynch, Extended generalized log-logistic families of lifetime distributions with an application, JPSS J. Probab. Stat. Sci. 8 (1), 1-17, 2010.
12. [12] I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, 7th ed., Academic Press, San Diego, 2000.
13. [13] J.F. Lawless, Statistical Models and Methods for Lifetime Data, Wiley, New York, 2003.
14. [14] M.C.S. Lima, F. Prataviera, E.M.M. Ortega and G.M. Cordeiro, The odd log-logistic geometric family with applications in regression models with varying dispersion, J. Stat. Theory Appl. 18, 278-294, 2019.
15. [15] A.N. Marshall and I. Olkin, A new method for adding a parameter to a family of distributions with applications to the exponential and Weibull families, Biometrika 84 (3), 641-652, 1997.
16. [16] G.S. Mudholkar and D.K. Srivastava, Exponentiated Weibull family for analyzing bathtub failure-rate data, IEEE Trans. Rel. 42 (2), 299-302, 1993.
17. [17] S. Nadarajah, G.M. Cordeiro and E.M.M. Ortega, The exponentiated Weibull distribution: a survey Statist. Papers 54 (3), 839-877, 2013.
18. [18] P.E. Oguntunde, O.A. Odetunmibi and A.O. Adejum, On the exponentiated generalized Weibull distribution: A generalization of the Weibull distribution, Indian J Sci Technol 8 (35), 1-7, 2015.
19. [19] E.M.M. Ortega, J.N. da Cruz and G.M. Cordeiro, The log-odd logistic-Weibull regression model under informative censoring, Model Assist Stat Appl 14 (3), 239-254, 2019.
20. [20] F. Prataviera, G.M. Cordeiro, E.M.M. Ortega and A.K. Suzuki, The odd log-logistic geometric normal regression models with applications, Adv. Data Sci. Adapt. Anal. 11 (01n02), 1-25, 2019.
21. [21] F. Prataviera, E.M.M. Ortega, G.M. Cordeiro and A.S. Braga, The heteroscedastic odd log-logistic generalized gamma regression model for censored data, Comm. Statist. Simulation Comput. 48 (6), 1815-1839, 2018.
22. [22] F. Prataviera, E.M.M. Ortega, G.M. Cordeiro, R.R. Pescim and B.A.W. Verssani, A new generalized odd log-logistic flexible Weibull regression model with applications in repairable systems, Reliab. Eng. Syst. Saf. 176, 13-26, 2018.
23. [23] J.C Souza Vasconcelos, G.M. Cordeiro, E.M.M. Ortega and E.G. Araújo, The new odd log-logistic generalized inverse gaussian regression model, J. Probab. Stat., 1-13, 2019.
24. [24] M.H. Tahir and S. Nadarajah, Parameter induction in continuous univariate distributions: Well-established G families, An. Acad. Brasil. Ciênc. 87 (2), 539-568, 2015.