Some comments on methodology of cubic rank transmuted distributions

Year 2020, Volume: 69 Issue: 2, 1161 - 1170, 31.12.2020

Mehmet Yılmaz Monireh Hameldarbandı

https://doi.org/10.31801/cfsuasmas.733922

Cited By: 1

Abstract

In this study, at first a new polynomial rank transmutation is proposed. Then, a new cubic rank transmutation is introduced by simplifying the set of transmutation parameters in order to improve its usefulness in statistical modeling. The purpose of this comment is to clarify some issues that exist in the methodology of obtaining the distribution by the cubic transmutation and the stage of proofing it. In this way, both the parameter space is expanded and the process of establishing the cubic transformed distribution family is given.

Keywords

Polynomial rank transmutation, cubic rank transmutation, quadratic rank transmutation, transmuted distribution family, order statistics, failure distribution

References

• Abd El Hady, N. E. (2014). Exponentiated transmuted weibull distribution a generalization of the weibull distribution. International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, 8(6):903 – 911.
• Alizadeh, M., Merovci, F., and Hamedani, G. G. (2017). Generalized transmuted family of distributions: properties and applications. Hacettepe Journal of Mathematics and Statistics, 46:645–667.
• Ashour, S. K. and Eltehiwy, M. A. (2013). Transmuted exponentiated lomax distribution. Aust J Basic Appl Sci, 7(7):658–667.
• Das, K. K. and Barman, L. (2015). On some generalized transmuted distributions. Int. J. Sci. Eng. Res, 6:1686–1691.
• Eltehiwy, M. and Ashour, S. (2013). Transmuted exponentiated modified weibull distribution. International Journal of Basic and Applied Sciences, 2(3):258–269.
• Eryilmaz, S. (2014). Computing reliability indices of repairable systems via signature. Journal of Computational and Applied Mathematics, 260:229 – 235.
• Franko, C., Ozkut, M., and Kan, C. (2015). Reliability of coherent systems with a single cold standby component. Journal of Computational and Applied Mathematics, 281:230 – 238.
• Granzotto, D., Louzada, F., and Balakrishnan, N. (2017). Cubic rank transmuted distributions: inferential issues and applications. Journal of Statistical Computation and Simulation, 87(14):2760–2778.
• Mansour, M. M., Enayat, M. A., Hamed, S. M., and Mohamed, M. S. (2015). A new transmuted additive weibull distribution based on a new method for adding a parameter to a family of distributions. Int. J. Appl. Math. Sci, 8:31–51.
• Mansour, M. M. and Mohamed, S. M. (2015). A new generalized of transmuted lindley distribution. Appl. Math. Sci, 9:2729–2748.
• Merovci, F. (2013). Transmuted exponentiated exponential distribution. Mathematical Sciences and Applications E-Notes, 1(2):112–122.
• Nofal, Z. M., Afify, A. Z., Yousof, H. M., and Cordeiro, G. M. (2017). The generalized transmuted-g family of distributions. Communications in StatisticsTheory and Methods, 46(8):4119–4136.
• Nofal, Z. M. and El Gebaly, Y. M. (2017). The generalized transmuted weibull distribution for lifetime data. Pakistan Journal of Statistics and Operation Research, 13(2):355–378.
• Rahman, M. M., Al-Zahrani, B., and Shahbaz, M. Q. (2018). A general transmuted family of distributions. Pakistan Journal of Statistics and Operation Research, 14(2).
• Saboor, A., Khan, M. N., Cordeiro, G. M., Pascoa, M. A., Ramos, P. L., and Kamal, M. (2019). Some new results for the transmuted generalized gamma distribution. Journal of Computational and Applied Mathematics, 352:165 – 180.
• Shaw, W. T. and Buckley, I. R. C. (2007). The alchemy of probability distributions: Beyond gram-charlier & cornish-fisher expansions, and skew-normal or kurtotic-normal distributions. Submitted, Feb, 7:64.
• Shaw, W. T. and Buckley, I. R. C. (2009). The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. ArXiv e-prints.
• Yilmaz, M., Potas, N., and Topcu, B. (2015). Reliability properties of systems with three dependent components. In Chaos, Complexity and Leadership 2013, pages 117–127. Springer.