Abstract
We introduce a new family of univariate continuous distributions called the Marshall–Olkin transmuted-G family which extends the transmuted-G family pioneered by Shaw and Buckley (2007). Special models for the new family are provided. Some of its mathematical properties including quantile measure, explicit expressions for the ordinary and incomplete moments, generating function, Rényi and Shannon entropies, order statistics and probability weighted moments are derived. The estimation of the model parameters is performed by maximum likelihood. The flexibility of the proposed family is illustrated by means of two applications to real data sets.
References
[1] A. Z. Afify, G. M. Cordeiro, H. M. Yousof, A. Saboor and E. M. M. Ortega, The Marshall–Olkin additive Weibull distribution with variable shapes for the hazard rate, Hacet. J. Math. Stat. 47 (2018), no. 2, 365–381. 10.15672/HJMS.201612618532Suche in Google Scholar
[2] A. Z. Afify, G. G. Hamedani, I. Ghosh, M. E. Mead, The transmuted Marshall–Olkin–Frechet distribution: Properties and applications, Int. J. Stat. Probab. 4 (2015), no. 4, 132–148. 10.5539/ijsp.v4n4p132Suche in Google Scholar
[3] A. Z. Afify, Z. M. Nofal and N. S. Butt, Transmuted complementary Weibull geometric distribution, Pak. J. Stat. Oper. Res. 10 (2014), no. 4, 435–454. 10.18187/pjsor.v10i4.836Suche in Google Scholar
[4] A. Z. Afify, Z. M. Nofal and A. E. H. N. Ebraheim, Exponentiated transmuted generalized Rayleigh distribution: A new four parameter Rayleigh distribution, Pak. J. Stat. Oper. Res. 11 (2015), no. 1, 115–134. 10.18187/pjsor.v11i1.873Suche in Google Scholar
[5] A. Z. Afify, Z. M. Nofal, H. M. Yousof, Y. M. El Gebaly and N. S. Butt, The transmuted Weibull Lomax distribution: Properties and application, Pak. J. Stat. Oper. Res. 11 (2015), no. 1, 135–152. 10.18187/pjsor.v11i1.956Suche in Google Scholar
[6] G. R. Aryal, Transmuted log-logistic distribution, J. Stat. Appl. Probab. 2 (2013), 11–20. 10.12785/jsap/020102Suche in Google Scholar
[7] G. R. Aryal and C. P. Tsokos, On the transmuted extreme value distribution with application, Nonlinear Anal. 71 (2009), no. 12, e1401–e1407. 10.1016/j.na.2009.01.168Suche in Google Scholar
[8] G. R. Aryal and C. P. Tsokos, Transmuted Weibull distribution: A generalization of the Weibull probability distribution, Eur. J. Pure Appl. Math. 4 (2011), no. 2, 89–102. Suche in Google Scholar
[9] S. K. Ashour and M. A. Eltehiwy, Transmuted exponentiated modified Weibull distribution, Internat. J. Basic Appl. Sci. 2 (2013), no. 3, 258–269. Suche in Google Scholar
[10] G. M. Cordeiro, E. M. M. Ortega and S. Nadarajah, The Kumaraswamy Weibull distribution with application to failure data, J. Franklin Inst. 347 (2010), no. 8, 1399–1429. 10.1016/j.jfranklin.2010.06.010Suche in Google Scholar
[11] I. Elbatal, Transmuted modified inverse Weibull distribution: A generalization of the modified inverse Weibull probability distribution, Internat. J. Math. Arch. 4 (2013), 117–129. Suche in Google Scholar
[12] M. S. Khan and R. King, Transmuted modified Weibull distribution: A generalization of the modified Weibull probability distribution, Eur. J. Pure Appl. Math. 6 (2013), no. 1, 66–88. Suche in Google Scholar
[13] C. Lee, F. Famoye and O. Olumolade, Beta-Weibull distribution: some properties and applications to censored data, J. Mod. Appl. Stat. Methods 6 (2007), no. 1, 173–186. 10.22237/jmasm/1177992960Suche in Google Scholar
[14] A. W. Marshall and I. Olkin, A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika 84 (1997), no. 3, 641–652. 10.1093/biomet/84.3.641Suche in Google Scholar
[15] Z. M. Nofal, A. Z. Afify, H. M. Yousof and G. M. Cordeiro, The generalized transmuted-G family of distributions, Comm. Statist. Theory Methods 46 (2017), no. 8, 4119–4136. 10.1080/03610926.2015.1078478Suche in Google Scholar
[16] D. N. Prabhakar Murthy, M. Xie and R. Jiang, Weibull Models, Wiley Ser. Probab. Stat., Wiley-Interscience, Hoboken, 2004. 10.1002/047147326XSuche in Google Scholar
[17] W. T. Shaw and I. R. C. Buckley, The alchemy of probability distributions: Beyond Gram–Charlier & Cornish–Fisher expansions, and skew-normal or kurtotic-normal distributions, preprint (2007), https://arxiv.org/abs/0901.0434. Suche in Google Scholar
© 2020 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- A Stochastic Control Model of Investment and Consumption with Applications to Financial Economics
- Bayesian Estimation of an M/M/𝑅 Queue with Heterogeneous Servers Using Markov Chain Monte Carlo Method
- The Reflected-Shifted-Truncated Lindley Distribution with Applications
- The Marshall–Olkin Transmuted-G Family of Distributions
- Time-Dependent Stress-Strength Reliability Models with Phase-Type Cycle Times
Artikel in diesem Heft
- Frontmatter
- A Stochastic Control Model of Investment and Consumption with Applications to Financial Economics
- Bayesian Estimation of an M/M/𝑅 Queue with Heterogeneous Servers Using Markov Chain Monte Carlo Method
- The Reflected-Shifted-Truncated Lindley Distribution with Applications
- The Marshall–Olkin Transmuted-G Family of Distributions
- Time-Dependent Stress-Strength Reliability Models with Phase-Type Cycle Times