Exponentiated Weibull-logistic distribution

In this paper, exponentiated Weibull-logistic distribution is introduced. The main functions of proposed distribution are derived and plotted for different parameter values. Besides, skewness and kurtosis measures of proposed distribution are presented. Then, by finding moment generating function, expected value and variance are derived. A simulation study is given for showing performance of exponentiated Weibull-logistic distribution by the maximum likelihood estimation approach. Finally, applications based on real datasets are presented and proved that, exponentiated Weibull-logistic distribution is better than existing distributions in literature.

Keywords:

Weibull-logistic distribution, Weibull-G family Maximum likelihood estimation, Hazard function,

PDF

___

Reference1: Ahmad, Z., Elgarhy, M., Hamedani, G. G. (2018). A new Weibull-X family of distributions: properties, characterizations and applications. Journal of Statistical Distributions and Applications, 5(5).
Reference2: Alizadeh, M., Rasekhi, M., Haitham M. Y., Hamedani, G. G. (2018). The transmuted Weibull-G family of distributions. Hacettepe Journal of Mathematics and Statistics, 47(6), 1671-1689.
Reference3: Bourguignon, M., Silva, R. B., Cordeiro, G. M. (2014). The Weibull-G family of probability distributions. Journal of Data Science, 12, 53-68.
Reference4: Bursa, N., Özel, G. (2017). The exponentiated Kumaraswamy-power function distribution. Hacettepe Journal of Mathematics and Statistics, 46(2), 277-292.
Reference5: Cordeiro, G. M., Ortega, E. M. M., Ramires, T. G. (2015). A new generalized Weibull family of distributions: mathematical properties and applications. Journal of Statistical Distributions and Applications, 2(13).
Reference6: Cordeiro, G. M., Afify, A. Z., Haitham M. Y., Pescim, R. R., Aryal, G. R. (2017). The exponentiated Weibull-H family of distributions: theory and applications. Mediterranean Journal of Mathematics, 14(4), 155.
Reference7: Elgarhy, M., Shakil, M., Kibria, B.M.G. (2017). Exponentiated Weibull-exponential distribution with applications. Communications Series A1: Mathematics and Statistics, 12(2), 710-725.
Reference8: Gurvich, M. R., DiBenedetto, A. T., Ranade, S. V. (1997). A new statistical distribution for characterizing the random strength of brittle materials. Journal of Materials Science, 32, 2559-2564.
Reference9: Hassan, A. S., Elgarhy, M. (2016). A new family of exponentiated Weibull-generated distributions. International Journal of Mathematics And its Applications, 4(1), 135-148.
Reference10: Hassan, A., Elgarhy, M. (2018). Exponentiated Weibull-Weibull distribution: statistical properties and applications. Gazi University Journal of Science, 68 (1), 248-270.
Reference11: Johnson, N. L., Kotz, S., Balakrishnan, N. (1995). Continuous univariate distributions. Wiley-Interscience, Volume 2, 2nd ed., USA.
Reference12: Korkmaz, M. Ç. (2018). Exponentiated Weibull-lomax distribution: properties and estimation. Journal of Data Science, 16(2), 277-298.
Reference13: Korkmaz, M. Ç. (2019). A new family of the continuous distributions: the extended Weibull-G family. Communications Series A1: Mathematics and Statistics, 68(1), 248-270.
Reference14: Nadarajah, S., Kotz, S. (2008). strength modeling using Weibull distributions. Journal of Mechanical Science and Technology, 22(7), 1247-1254.
Reference15: Nassar, M. M., Radwan, S. S., Elmasry, A. (2017). Transmuted Weibull logistic distribution. International Journal of Innovative Research & Development, 6(4), 122-131.
Reference16: Smith, R. L., Naylor, J. C. (1987). A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. Journal of the Royal Statistical Society - Series C (Applied Statistics), 36(3), 358-369.
Reference17: Tahir, M. H., Zubair, M., Mansoor, M., Cordeiro, G. M., Alizadeh, M., Hamedani, G. G. (2016a). A new Weibull-G family of distributions. Hacettepe Journal of Mathematics and Statistics, 45(2) 629-647.
Reference18: Tahir, M. H., Alizadeh, M., Mansoor, M., Cordeiro, G. M., Zubair, M., A. (2016b). The Weibull-power function distribution with applications. International Journal of Innovative Research & Development, 45(1), 245-265.
Reference19: Weibull, W. (1951). A statistical distribution function of wide applicability. Journal of Applied Mechanics, 18, 293-297.