Main Article Content
Abstract
A new class of distributions called Marshall-Olkin Zubair-G family is proposed in this study. Some statistical properties of the family are derived and two special distributions namely, Marshall-Olkin Zubair Nadarajah-Haghighi and Marshall-Olkin Zubair Weibull distributions are developed. The plots of the density and hazard rate functions of the special distributions exhibit different shapes for chosen parameter values, making them good candidates for modeling different types of datasets. A real life application using the Marshall-Olkin Zubair Nadarajah-Haghighi distribution revealed that it performs better than other existing extensions of the Nadarajah-Haghighi distribution for the given dataset.
Keywords
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following License
CC BY: This license allows reusers to distribute, remix, adapt, and build upon the material in any medium or format, so long as attribution is given to the creator. The license allows for commercial use.
References
- Abdul-Moniem, I. B. (2015). Exponentiated Nadarajah and Haghighi's exponential distribution. International Journal of Mathematical Analysis and Applications, 2(5): 68-73.
- Bolker, B. (2014). Tools for general maximum likelihood estimation. R development core team.
- Cordeiro, G. M. and de Castro, M. (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81(7): 883-898.
- Haq, M. A. and Elgarhy, M. (2018). The odd Fréchet-G family of probability distributions. Journal of Statistics Applications and Probability, 7(1): 189-203.
- Jamal, F., Tahir, M. H., Alizadeh, M. and Nasir, M. A. (2017). On Marshall-Olkin Burr X family of distributions. Tbilisi Mathematical Journal, 10(4): 175-199.
- Lee, E. T. and Wang, J. (2003). Statistical methods for survival data analysis. Volume 476. John Wiley and Sons.
- Lima, S. R. L. (2015). The half normal generalized family and Kumaraswamy Nadarajah-Haghighi distribution. Master thesis, Universidade Federal de Pernumbuco.
- Mahdavi, A. and Kundu, D. (2017). A new method for generating distributions with an application to exponential distribution. Communications in Statistics-Theory and Methods, 46(13): 6543-6557.
- Marshall, A. W. and Olkin, I. (1997). A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika, 84:641-652.
- MirMostafaee, S. M. T. K., Mahdizadeh, M. and Lemonte, A. J. (2017). The Marshall-Olkin extended generalized Rayleigh distribution: Properties and applications. Communications in Statistics: Theory and Methods, 46: 653-671.
- Nasir, M. A., Jamal, F., Silva, G. O. and Tahir, M. H. (2018). Odd Burr-G Poisson family of distributions. Journal of Statistics Applications and Probability, 7(1): 9-28.
- Nasiru, S. (2018). Extended odd Fréchet-G family of distributions. Journal of Probability and Statistics, 2018: 1-12.
- Nasiru, S., Mwita, P. N. and Ngesa, O. (2017). Exponentiated generalized transformed-transformer family of distributions. Journal of Statistical and Econometric Methods, 6(4): 1-17.
- Nassar, M. Kumar, D., Dey, S., Cordeiro, G. M. and Afify, A. Z. (2019). The Marshall-Olkin alpha power family of distributions with applications. Journal of Computational and Applied Mathematics, 351: 41-53.
- Rényi, A. (1961). On measures of entropy and information. In proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability. Pages 547-561, University of California Press.
- Zubair, A. (2018). The Zubair-G family of distributions: properties and applications. Annals of Data Science. http://doi.org/10.1007/s40745-018-0169-9.