On the Families of Generalized Exponentiated Weibull Distributions: Properties and Applications

Anyiam Kizito Ebere^1, , Onyeagu Sydney Iheanyi² and Njoku Modestus Onyekachi¹

¹Department of Statistics, School of Physical Sciences, Federal University of Technology, Owerri, Imo State, Nigeria

²Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, Awka, Anambra State, Nigeria

Cite this paper:
Anyiam Kizito Ebere, Onyeagu Sydney Iheanyi and Njoku Modestus Onyekachi. On the Families of Generalized Exponentiated Weibull Distributions: Properties and Applications. Turkish Journal of Analysis and Number Theory. 2021; 9(3):52-64. doi: 10.12691/tjant-9-3-4

Abstract

Some new families of exponentiated Weibull (EW) distribution named T-Exponentiated Weibull{Y} using the T-R{Y} context are presented in this article. The quantile functions of five notable distributions, namely, Logistic, Log-Logistic, Rayleigh, Exponential and Lomax were used to develop five sub-families T-EW{Logistic}, T-EW{Log-Logistic}, T-EW{Rayleigh}, T-EW{Exponential} and T-EW{Lomax} and some general properties such as the quantile functions, Moments, mean deviations from the mean and median, Shannon entropies are obtained. The shapes of the exponentiated Weibull family densities shows can be unimodal, bimodal, monotonically decreasing, skewed to the left, skewed to the right and almost symmetric curves while the hazard function can be bathtub shaped, up-side down bathtub shaped, and increasing-deceasing-increasing. To demonstrate the flexibility and usefulness of the model, three real-life datasets analyzed and the results compared with some competing models.

Keywords:
T-R{Y} family quantile function moments Shannon entropy

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References:

[1]	Johnson, N. L. (1949). “Systems of frequency curves generated by method of translation”. Biometrika, 36(1/2): 149-176.
[2]	Chakraborty, S. and Hazarika, P. J. (2011). A survey of the theoretical developments in univariate skew-normal distribution. Assam Statistical. Review, 25:41-65.
[3]	Tahir, M. H. and Cordeiro, G. M. (2016). Compounding of distributions: a survey and new generalized classes. Journal of Statistical Distributions and Applications, 3: 13, 1-35.
[4]	Bhatti, F. A., Hamedani, G. G., Najibi, S. M. and Ahmad, M. (2019). On the Extended Chen Distribution: Development, Properties, Characterizations and Applications. Annals of Data Science. 1-22.
[5]	Mudholkar,G. S. and Srivastava, D. K. (1993). Exponentiated Weibull for analyzing bathtub failure-rate data. IEEE Transactions on Reliability. 42(2), 299-302.
[6]	Alzaatreh, A. Lee, C, Famoye, F. and Ghosh, I. (2016). The Generalized Cauchy family of distributions with Applications. Journal of Statistical Distributions and Applications, Springer, Vol.3(1), 1-16.
[7]	Mahmoud, A., Lee, C. and Famoye, F. (2017). Families of distributions arising from the quantile of generalized lambda distribution. Journal of Statistical Distributions and Applications. 4:25, 1-28.
[8]	Yousof, H. M, Alizadeh, M, Jahanshahi, S. M. A, Ramires, T. G., Ghosh, I. and Hamedani, G. G. (2017). The transmuted Topp-Leone G family of distributions: Theory, characterizations and applications. Journal of Data Science, 15,723-740.
[9]	Hamed, D., Famoye, F. and Lee, C. (2018). On families of generalized Pareto distributions: Properties and Applications. Journal of Data Science, 16(2), 377-396.
[10]	Zubair, M., Alzaatreh, A., Cordeiro, G. M., Tahir, M. H. and Mansoor, M.(2018). On the generalized classes of exponential distribution using T-X family framework. Faculty of Sciences and Mathematics, University of Nis, Serbia, Filomat 32:4, 1259-1272.
[11]	Aldeni, M, Famoye, F. and Lee, C. (2020). A generalized family of lifetime distributions with survival models. Journal of Modern Applied Statistical Methods Vol. 18, No.2 eP2944.
[12]	Aljarrah, M. A., Lee, C. and Famoye, F. (2014). On T-X family of distributions using quantile functions. Journal of Statistical Distributions and Applications, 1(2), 1-17.
[13]	Alzaatreh, A., Lee, C. and Famoye, F. (2014). T-normal family of distributions: A new approach to generalize the normal distribution. Journal of Statistical Distributions and Applications, 1: 16.
[14]	Gradshteyn, I. S. and Ryhzik, I. M. (1965). Tables of integrals, series and products. Academic Press, New York.
[15]	Anyiam, K. E. and Onyeagu, S. I. (2021). Gumbel-Exponentiated Weibull{Logistic} lifetime distribution and its applications. Open Journal of Statistics, Vol.11, No.5, 817-837.
[16]	Al-Aqtash, R., Lee, C. and Famoye, F. (2014). Gumbel-Weibull distribution: Properties and application. Journal of Modern Applied Statistical Method, 13, 201-225.
[17]	Cook, R.D. and Weisberg, S. (1994). An Introduction to Regression Graphics. New York: John Wiley & Sons, Inc.
[18]	Andrews, D. F. and Herzberg, A. M. (1985). Data: a collection of problems from many fields for students and research worker. Springer Science and Business Media..
[19]	Osatohanmwen, P., Oyegue, F.O. and Ogbonmwan, S.M. (2019). A New Member from the T-X Family of Distributions: The Gumbel-Burr XII distribution and its Properties. Sankhya A, Vol. 81, pp. 298-322.