A NEW ALTERNATIVE SELECTION CRITERION FOR FAMILY OF SOME TRANSMUTED DISTRIBUTIONS BASED ON EXPONENTIAL DISTRIBUTION

Öz

Although Akaike information criterion is the most popular selection criterion in the literature, it gives inconsistent results in determining the correct model according to other selection criteria in transmuted distribution families. We motivate a new extension of the Akaike information criterion in the solution of this problem. In this paper, we suggest a new selection criterion as an alternative to the Akaike information criterion for the family of transmuted distribution. We discuss special cases of this family based on exponential distribution. A Monte Carlo simulation study is considered to compare the performances of this new criterion with the Akaike information criterion. Also, a numerical example is presented.

Anahtar Kelimeler

• Akaike information criterion
• Modified Akaike information criterion
• Monte Carlo simulation
• Transmuted family

Kaynakça

1. Karakaya, K., Kınacı, İ., Kuş, C., Akdoğan, Y., “A new family of distributions”, Hacettepe Journal of Mathematics and Statistics. 46(2): 303-314, 2017.
2. Korkmaz, M.Ç., “A new family of the continuous distributions: the extended Weibull-G family”, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1): 248-270, 2018.
3. Korkmaz, M.Ç., Yousof, H.M., Hamedani, G.G. "The exponential Lindley odd log-logistic-G family: Properties, characterizations and applications", Journal of Statistical Theory and Applications. 17(3): 554-571, 2018.
4. Rahman, M. M., AlZahrani, B., Shahbaz, M.Q., “A general transmuted family of distributions”, Pakistan Journal of Statistics and Operation Research. 451-469, 2018.
5. Pavlov, N., Iliev, A., Rahnev, A., Kyurkchiev, N., “Some transmuted software reliability models” Journal of Mathematical Sciences and Modelling. 2(1): 64-70, 2018.
6. Riffi, M.I., “Higher rank transmuted families of distributions”, IUG Journal of Natural Studies. 27(2) ,2019.
7. Ahmad, Z., Hamedani, G. G., Butt, N. S., “Recent developments in distribution theory: a brief survey and some new generalized classes of distributions”, Pakistan Journal of Statistics and Operation Research. 87-110, 2019.
8. Rahman, M.M., Al-Zahrani, B., Shahbaz, S. H., Shahbaz, M.Q., “Transmuted Probability Distributions: A Review” Pakistan Journal of Statistics and Operation Research. 83-94, 2020.

9. Proschan, F. Theoretical explanation of observed decreasing failure rate.Technometrics5:375–383, 1963.
10. Dahiya, R. C., Gurland, J. Goodness of fit tests for the gamma and exponential distributions. Technometrics (14), 791–801, 1972.
11. Gleser, L. J. The gamma distribution as a mixture of exponential distributions. The American Statistician, 43(2), 115–117, 1989.
12. Kus, C. A new lifetime distribution.Computational Statistics and Data Analysis, 5(1), 4497–4509, 2007.
13. Habibi, M., Asgharzadeh, A.. Power binomial exponential distribution: Modeling, simulation and application. Communications in Statistics-Simulation and Computation, 47(10), 3042-3061, 2018.