The Extended Odd Weibull-G Family: Properties and Applications

Abstract

The Weibull distribution is one of the most popular and widely used model for failure time in life-testing and reliability theory. In this study, we introduce a new class of continuous distributions called the extended odd Weibull-G family. Special models of new family are provided. Various structural properties including explicit expressions for the ordinary and incomplete moments, generating function, Rényi and Shannon entropies, order statistics and probability weighted moments are derived. The maximum likelihood method is used for estimating model parameters. The flexibility of the generated family is illustrated by means of two applications to real data sets.

Keywords

• Generating Function,maximum likelihood,moments,order statistics,Weibull distribution

References

1. Alizadeh, M., Cordeiro, G. M., Nascimento, A. D., Lima, M. D. C. S. and Ortega, E. M., Odd-Burr generalized family of distributions with some applications. Journal of Statistical Computation and Simulation, 87(2), (2017) 367--389.
2. Alexander, C., Cordeiro, G. M., Ortega, E. M. M. and Sarabia, J. M., Generalized beta generated distributions. Computational Statistics and Data Analysis, 56, (2012) 1880--1897.
3. Alzaatreh, A., Famoye, F. and Lee, C., A new method for generating families of continuous distributions. Metron, 71, (2013) 63--79.
4. Bourguignon, M., Silva, R.B., Cordeiro, G.M., The Weibull-G family of probability distributions. Journal of Data Science, 12, (2014) 53--68.
5. Braga, A.S. Cordeiro, G.M., Ortega, E.M.M., Cruz, N., The odd log-"logistic normal distribution: Theory and applications in analysis of experiments. Journal of Statistical Theory and Practice, 10, (2016) 311--335.
6. Chen, G. and Balakrishnan, N., A general purpose approximate goodness-of-fit test. Journal of Quality Technology, 27, (1995) 154--161.
7. Cordeiro, G. M., Ortega, E. M. M. and Nadarajah, S., The Kumaraswamy Weibull distribution with application to failure data. Journal of the Franklin Institute, 347, (2010) 1399--1429.
8. Cordeiro, G. M. and de Castro, M., A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81, (2011) 883-898.

9. Cordeiro, G. M., Hashimoto, E. M., Ortega, E. M., & Pascoa, M. A., The McDonald extended distribution: properties and applications. AStA Advances in Statistical Analysis, 96(3), (2012) 409--433.
10. Cordeiro, G. M., Alizadeh, M. and Ortega, E. M. M., The exponentiated half-logistic family of distributions: properties and applications. Journal of Probability and Statistics, 81, (2014), 1--21.
11. Cordeiro, G. M., Alizadeh, M., Tahir, M. H., Mansoor, M.,Bourguignon, M. and Hamedani, G. G. The beta odd log-logistic family of distributions. Hacettepe Journal of Mathematics and Statistics, forthcoming. (2015).
12. Cordeiro, G. M., Alizadeh, M., Ozel, G., Hosseini, B., Ortega, E. M. M. and Altun, E., The generalized odd log-logistic family of distributions: properties, regression models and applications. Journal of Statistical Computation and Simulation, 87(5), (2017), 908--932.
13. Eugene, N., Lee, C. and Famoye, F., Beta-normal distribution and its applications. Communications in Statistics-Theory and Methods, 31, (2002) 497--512.
14. Gauss, C. F., Theoria motvs corporvm coelestivm in sectionibvs conicis Solem ambientivm [Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections] (in Latin). (1809).
15. Gleaton, J. U. and Lynch, J. D., Properties of generalized log-logistic families of lifetime distributions. Journal of Probability and Statistical Science, 4(1), (2006) 51--64.
16. Gitifar, N., Rezaei, S. and Nadarajah,S., Compound distributions motivated by linear failure rate. SORT, 40, (2016) 177--200.
17. Gradshteyn, I.S. and Ryzhik, I.M,. Table of Integrals, Series, and Products. Academic Press. (2000).
18. Hong, Y. and Meeker, W.Q., Field-failure predictions based on failure-time data with dynamic covariate information. Technometrics, 55, (2013) 135--149.
19. Marshall, A. W. and Olkin, I., A new methods for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika, 84, (1997) 641--652.
20. Oguntunde, P. E., Odetunmibi, O. A. and Adejumo, A. O., On the exponentiated generalized Weibull distribution: A generalization of the Weibull distribution . Indian Journal of Science and Technology, 8. (2015).
21. Proschan, F., Theoretical explanation of observed decreasing failure rate, Technometrics 5, (1963) 375--383.
22. Shaw, W. T. and Buckley, I. R. C., The alchemy of probability distributions: beyond Gram-Charlier expansions and a skew-kurtotic-normal distribution from a rank transmutation map. Research Report. (2007).
23. Zografos, K. and Balakrishnan, N., On families of beta and generalized gamma generated distributions and associated inference. Statistical Methodology, 6, (2009) 344--362.
24. Weibull, W., A statistical distribution function of wide applicability, Journal of Applied Mechanics, 18, (1951) 293--297.