Volume 20, Issue 2 (12-2021)                   JIRSS 2021, 20(2): 129-152 | Back to browse issues page

XML Print

Universite de Caen, LMNO, Campus II, Science 3, 14032, Caen, France. , christophe.chesneau@gmail.com
Abstract:   (609 Views)

Finding new families of distributions has become a popular tool in statistical research. In this article, we introduce a new flexible four-parameter discrete model based on the Marshall-Olkin approach, namely, the discrete Kumaraswamy Marshall-Olkin exponential distribution. The proposed distribution can be viewed as another generalization of the geometric distribution and enfolds some important distributions as special cases. Some properties of the new distribution are derived. The model parameters are estimated by the maximum likelihood method, with validation through a complete simulation study. The usefulness of the new model is illustrated via count-type real data sets.

Full-Text [PDF 277 kb]   (686 Downloads)    
Type of Study: Original Paper | Subject: 62Exx: Distribution theory
Received: 2020/07/24 | Accepted: 2022/02/1 | Published: 2022/04/12

1. Aarset, M. V. (1987), How to identify a bathtub hazard rate. IEEE Transactions on Reliability , 36(1), 106-108. [DOI:10.1109/TR.1987.5222310]
2. Akinsete, A., Famoye, F., and Lee, C. (2014), The Kumaraswamy-geometric distribution. Journal of Statistical Distributions and Applications, 1, 1-21. [DOI:10.1186/s40488-014-0017-1]
3. Alizadeh, M. Tahir, M. H., Cordeiro, G. M., Zubair, M., and Hamedani, G. G. (2015), The Kumaraswamy Marshall-Olkin family of distributions. Journal of the Egyptian Mathematical Society , 23(3), 546-557. [DOI:10.1016/j.joems.2014.12.002]
4. Alzaatreh, A., Lee, C., and Famoye, F. (2012), On the discrete analogues of continuous distributions. Statistical Methods , 9(6), 589-603. [DOI:10.1016/j.stamet.2012.03.003]
5. Amigo, J. M., Balogh, S. G., and Hernandez, S. (2018), A brief review of generalized entropies. Entropy , 20, 813. [DOI:10.3390/e20110813]
6. Chakraborty, S. (2015), A new discrete distribution related to generalized gamma distribution and its properties. Communication in Statistics-Theory and Methods , 44(8), 1691-1705. [DOI:10.1080/03610926.2013.781635]
7. Chakraborty, S., and Chakravarty, D. (2016), A new discrete probability distribution with integer support on (-∞,∞). Communication in Statistics-Theory and Method , 45(2), 492-505. [DOI:10.1080/03610926.2013.830743]
8. Cordeiro, G. M., and de Castro, M. (2011), A new family of generalized distributions. Journal of Statistics Computation and Simulation , 81(7), 883-893. [DOI:10.1080/00949650903530745]
9. Cox, D. R., and Hinkley, D. V. (1974), Theoretical Statistics, London: Chapman & Hall. [DOI:10.1007/978-1-4899-2887-0]
10. Gomez-Deniz, E. (2010), Another generalization of the geometric distribution. Test , 19(2), 399-415. [DOI:10.1007/s11749-009-0169-3]
11. Gupta, R. C., and Gupta, R. D. (2007), Proportional reversed hazard rate model and its applications. Journal of Statistics and Planning Inference , 137(11), 3525-3536. [DOI:10.1016/j.jspi.2007.03.029]
12. Gupta, R. C., Gupta, P. L., and Gupta, R. D. (1998), Modeling failure time data by Lehman alternatives. Communications in Statistics-Theory Methods , 27(4), 887-904. [DOI:10.1080/03610929808832134]
13. Jayakumar, K., and Thomas, M. (2008), On a generalization of Marshall-Olkin scheme and its application to Burr type XII distribution. Statistical Papers , 49(3), 421-439. [DOI:10.1007/s00362-006-0024-5]
14. Jayakumar, K., and Sankaran, K. K. (2017a), A discrete generalization of Marshall-Olkin scheme and its application to geometric distribution. Journal of the Kerala Statistical Association , 28, 1-21.
15. Jayakumar, K., and Sankaran, K. K. (2017b), A generalization of discrete Weibull distribution. Communications in Statistics-Simulation and Computation , 47(24), 6064-6078. [DOI:10.1080/03610926.2017.1406115]
16. Krishna, H., and Pundir, P. S. (2009), Discrete Burr and discrete Pareto distributions. Statistical Methodology , 6(2), 177-188. [DOI:10.1016/j.stamet.2008.07.001]
17. Lisman, J. H. C., and van Zuylen, M. C. A. (1972), Note on the generation of the most probable frequency distribution. Statistica Neerlandica , 26(1), 19-23. [DOI:10.1111/j.1467-9574.1972.tb00152.x]
18. 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. Biometrica , 84(3), 641-652. [DOI:10.1093/biomet/84.3.641]
19. Murthy, D. N. P., Xie, M., and Jiang, R. (2004), Weibull models. New Jersey: John Wiley and Sons.
20. Nakagawa, T., and Osaki, S. (1975), The discrete Weibull distribution. IEEE Transactions on Reliability , 24(5), 300-301. [DOI:10.1109/TR.1975.5214915]
21. Sato, H., Ikota, M., Aritoshi, S., and Masuda, H. (1999), A new defect distribution meteorology with a consistent discrete exponential formula and its applications. IEEE Transactions on Semiconductor Manufacturing , 12(4), 409-418. [DOI:10.1109/66.806118]
22. Stein, W. E., and Dattero, R. (1984), A new discrete Weibull distribution. IEEE Transactions on Reliability , 33(2), 196-197. [DOI:10.1109/TR.1984.5221777]
23. Steutel, F. W., and van Harn, K. (2004), Infinite Divisibility of Probability Distributions on the Real Line. New York: Marcel Dekker. [DOI:10.1201/9780203014127]
24. Supanekar, S. R., and Shirke, D. T. (2015), A new discrete family of distributions. ProbStat Forum , 8, 83-94.
25. Tahir, M. H., and Nadarajah, S. (2015), Parameter induction in continuous univariate distributions: Well established G families. Annals of the Brazilian Academy of Sciences , 87(2), 539-568. [DOI:10.1590/0001-3765201520140299]
26. Xie, M., and Goh, T. N. (1993), Improvement detection by control charts for high yield processes. International Journal of Quality & Reliability Management , 10(7), 24-31. [DOI:10.1108/02656719310043779]

Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.