ON DEVELOPMENT OF EXPONENTIATED FRECHET WEIBULL DISTRIBUTION: PROPERTIES AND APPLICATIONS
Main Article Content
Abstract
The Exponentiated Fréchet-Weibull (EF-Weibull) distribution is introduced as a flexible statistical model that extends the classical Fréchet and Weibull distributions by incorporating additional shape and scale parameters. This study derives its probability density function (PDF), cumulative distribution function (CDF), quantile function, hazard function, and moment-based properties, providing a comprehensive theoretical foundation. Maximum likelihood estimation (MLE) was employed for parameter estimation, ensuring its applicability to real-world datasets. A comparative analysis was conducted against the Exponentiated Fréchet (Exp-Fréchet), Exponentiated Weibull (Exp-Weibull), Exponentiated Exponential (Exp-Exponential), Fréchet, and Weibull distributions using loglikelihood (LL), Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Kolmogorov-Smirnov (KS) test, Anderson-Darling (AD) test, and Cramér-von Mises (CS) test. The results showed that the EF-Weibull distribution provided the best fit, achieving the highest LL and lowest AIC and BIC values, while also demonstrating superior empirical performance through KS, AD, and CS test statistics. Graphical evaluations, including histogram density plots, hazard function plots, and empirical CDF comparisons, further validated its modelling efficiency. The study concludes that the EF-Weibull distribution is an effective model for reliability analysis, survival analysis, and extreme value modelling.
Downloads
Article Details
Issue
Section
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
How to Cite
References
Baharith, L. A., & Alamoudi, H. H. (2021). The Exponentiated Fréchet-G family of distributions: Properties and applications. Journal of Statistical Theory and Applications, 20(3), 125-142.
Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer.
Cordeiro, G. M., Ortega, E. M. M., & Silva, G. O. (2015). The exponentiated generalized class of distributions. Journal of Statistical Computation and Simulation, 85(7), 1321-1344.
Elbatal, I. and Muhammed, H.Z. (2014). Exponentiated generalized inverse Weibull distribution. Applied Mathematical Sciences, 8, 3997-4012.
Eugene and Jones, M. C. (2008). Kumaraswamy's distribution: A beta-type distribution with some tractability advantages. Statistical Methodology. 6:70-81.
Galton, F. (1883). Enquiries into Human Faculty and its Development, Macmillan and Company, London.
Gompertz, B. (1825). On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society London, 115, 513-585.
Gupta, R.C., Gupta, P.L. and Gupta, R.D. (1998). Modeling failure time data by Lehman alternatives. Communications in Statistics, Theory and Methods, 27, 887-904.
Gupta, R.D. and Kundu, D. (1999). Generalized exponential distributions. Australian & New Zealand Journal of Statistics, 41(2), 173-188. 358 On Development of Four-Parameter Exponentiated Generalized.
Mudholkar, G. S., & Srivastava, D. K. (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Transactions on Reliability, 42(2), 299-302.
Nadarajah, S., & Kotz, S. (2003). Extreme value distributions: Theory and applications. International Statistical Review, 71(1), 31-47.
Nofal, Z. M., El-Gohary, A., & Alzaatreh, A. (2016). The T-X family of distributions: Properties and applications. Communications in Statistics - Theory and Methods, 45(4), 1090-1105.
Sahai, H., Bakouch, H. S., & El-Gohary, A. (2021). A new lifetime distribution with bathtub-shaped hazard rate: Properties and applications. Journal of Applied Statistics, 48(1), 37–56.
Smith, R. L., & Naylor, J. C. (1987). A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. Applied Statistics, 36(3), 358–369.
Weibull, W. (1951). A statistical distribution function of wide applicability. Journal of Applied Mechanics, 18(3), 293-297.