The Three-Parameter Exponentiated Weibull Exponential Distribution: Theoretical Properties and Practical Implications

doi:10.1007/s42967-025-00503-4

Abstract

Abstract: Various statistical properties of the exponentiated Weibull exponential (EWE) distribution including quantile and hazard rate functions, skewness, kurtosis, order statistics, and entropies are investigated. The parameters are estimated by the maximum likelihood estimation (MLE) method. The flexibility and behaviour of the estimators were studied through a simulation. The empirical flexibility of the presented distribution was examined by means of real-life data. It was observed that our distribution serves as a viable alternative model to existing probability densities in the literature for the analysis of lifetime data.

Key words: Maximum likelihood estimation (MLE), Moments, Orders statistics, Weibull distribution

Sandra S. Ferreira, Dário Ferreira. The Three-Parameter Exponentiated Weibull Exponential Distribution: Theoretical Properties and Practical Implications[J]. Communications on Applied Mathematics and Computation, 2026, 8(4): 1324-1350.

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URL: https://www.camc.shu.edu.cn/EN/10.1007/s42967-025-00503-4

https://www.camc.shu.edu.cn/EN/Y2026/V8/I4/1324

[1] Abbas, S., Farooq, M., Darwish, J.A., Ahmad, K., Shahbaz, M., Awan, M.Z.: Truncated Weibull-exponential distribution: methods and applications. Sci. Rep. 13, 20849 (2023). https://doi.org/10.1038/s41598-023-47899-z
[2] Abdullahi, U.A., Suleiman, A.A., Ishaq, A.I., Usman, A., Suleiman, A.: The Maxwell-exponential distribution: theory and application to lifetime data. Journal of Statistical Modeling & Analytics (JOSMA) 3(2), 1-15 (2021)
[3] Afify, A.Z., Cordeiro, G.M., Ortega, E.M.M., Yousof, H.M., Butt, N.S.: The four-parameter burst Birnbaum-Saunders distribution: properties, inference and application. Hacettepe Journal of Mathematics and Statistics 47(5), 1043-1066 (2018). https://doi.org/10.15672/HJMS.2018.559
[4] Ahmed, M.A., Mahmoud, M.R., ElSherbini, E.A.: The new Kumaraswamy-Kumaraswamy family of generalized distributions with application. Pakistan Journal of Statistics and Operation Research 11(2), 159-180 (2015). https://doi.org/10.18187/pjsor.v11i2.969
[5] Alahmadi, A., Alqawba, A., Almutiry, M., Shawki, W.A., Alrajhi, A.W., Al-Marzouki, S., Elgarhy, M.: A new version of weighted Weibull distribution: modelling to COVID-19 data. Discrete Dynamics in Nature and Society 2022, 3994361 (2022). https://doi.org/10.1155/2022/3994361
[6] Al-Dayian, G., El-Helbawy, A., Rezk, H.: Statistical inference for a simple constant stress model based on censored sampling data from the Kumaraswamy Weibull distribution. International Journal of Statistics and Probability 3(3), 80-89 (2014). https://doi.org/10.5539/ijsp.v3n3p80
[7] Al-Sulami, D.: Exponentiated exponential Weibull distribution: mathematical properties and application. Am. J. Appl. Sci. 17(4), 188-195 (2020). https://doi.org/10.3844/ajassp.2020.188.195
[8] Anakha, K.K., Chacko, V.: On exponential-Weibull distribution useful in reliability and survival analysis. International Journal of Scientific Research 15(1), 20-32 (2020)
[9] Bilal, M., Mohsin, M., Aslam, M. Weibull-exponential distribution and its application in monitoring industrial process. Mathematical Problems in Engineering 2021, 1-13 (2021). https://doi.org/10.1155/2021/3215432
[10] Bourguignon, M., Silva, R.B., Cordeiro, G.M.: The Weibull-G family of probability distributions. Journal of Data Science 12(1), 53-68 (2014)
[11] Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)
[12] Casella, G., Berger, R.L.: Statistical Inference. Duxbury Press, Belmont (2002)
[13] Cordeiro, G.M., de Castro, M.: A new family of generalized distributions. J. Stat. Comput. Simul. 81(7), 883-898 (2011). https://doi.org/10.1080/00949650903426221
[14] Cordeiro, G.M., Ortega, E.M., Nadarajah, S.: The Kumaraswamy Weibull distribution with application to failure data. J. Franklin Inst. 347(8), 1399-1429 (2010). https://doi.org/10.1016/j.jfranklin.2010.06.010
[15] Cordeiro, G.M., Ortega, E.M., da Cunha, D.C.C.: The exponentiated generalized class of distributions. Journal of Data Science 11(1), 1-27 (2013)
[16] Deepthy, G.S., Sebastian, N., Chandra, N.: Applications of Burr III-Weibull quantile function in reliability analysis. Statistical Theory and Related Fields 7(4), 296-308 (2023). https://doi.org/10.1080/24754269.2023.2201096
[17] El-Helbawy, A.A.A., Al-Dayian, G.R., Rezk, H.R.: Bayesian approach for constant-stress accelerated life testing for Kumaraswamy Weibull distribution with censoring. Pakistan Journal of Statistics and Operation Research 12(3), 407-428 (2016). https://doi.org/10.18187/pjsor.v12i3.1171
[18] Elgarhy, M., Shakil, M., Golam Kibria, B.M.: Exponentiated Weibull-exponential distribution with applications. Applications and Applied Mathematics. An International Journal (AAM) 12(2), 437-460 (2017)
[19] Eugene, N., Lee, C., Famoye, F.: Beta-normal distribution and its applications. Communications in Statistics-Theory and Methods 31(4), 497-512 (2002). https://doi.org/10.1081/STA-120003130
[20] Fachini-Gomes, J.B., Ortega, E.M., Cordeiro, G.M., Suzuki, A.K.: The bivariate Kumaraswamy Weibull regression model: a complete classical and Bayesian analysis. Communications for Statistical Applications and Methods 25(5), 523-544 (2018). https://doi.org/10.29220/CSAM.2018.25.5.523
[21] Gupta, R.C., Gupta, R.D., Gupta, P.L.: Modeling failure time data by Lehman alternatives. Communications in Statistics-Theory and Methods 27(4), 887-904 (1998)
[22] Gupta, R.D., Kundu, D.: Generalized exponential distributions. Aust. N. Z. J. Stat. 41(2), 173-188 (1999). https://doi.org/10.1111/1467-842X.00084
[23] Gupta, R.D., Kundu, D.: Exponentiated exponential family: an alternative to gamma and Weibull distributions. Biom. J. 43(1), 117-130 (2001)
[24] Hassan, A.S., Elgarhy, M.: A new family of exponentiated Weibull-generated distributions. International Journal of Mathematics and Its Applications 4, 135-148 (2016)
[25] Horn, R.A., Johnson, C.R.: Matrix Analysis (2nd ed.). Cambridge University Press, Cambridge (2012). https://doi.org/10.1017/CBO9780511810817
[26] Jiang, R., Murthy, D.N.P.: The exponentiated Weibull family: a graphical approach. IEEE Trans. Reliab. 48(1), 68-72 (1999). https://doi.org/10.1109/24.765927
[27] Jones, M.C.: Kumaraswamy’s distribution: a beta-type distribution with some tractability advantages. Statistical Methodology 6(1), 70-81 (2009). https://doi.org/10.1016/j.stamet.2008.04.001
[28] Lawless, J.F: Statistical Models and Methods for Lifetime Data (2nd ed.). John Wiley & Sons, Inc., Hoboken, New Jersey (2011)
[29] Mastor, S., Ngesa, O., Mung’atu, J., Alfaer, N.M., Afify, A.Z.: The extended exponential Weibull distribution: properties, inference, and applications to real-life data. Journal of Mathematics 2022, 4068842, (2022). https://doi.org/10.1155/2022/4068842
[30] Mudholkar, G.S., Hutson, A.D.: The exponentiated Weibull family: some properties and a flood data application. Communications in Statistics-Theory and Methods 25(12), 3059-3083 (1996). https://doi.org/10.1080/03610929608831812
[31] Mudholkar, G.S., Srivastava, D.K.: Exponentiated Weibull family for analyzing bathtub failure rate data. IEEE Trans. Reliab. 42(2), 299-302 (1993). https://doi.org/10.1109/24.229504
[32] Mudholkar, G.S., Srivastava, D.K., Freimer, M.: The exponentiated Weibull family: a reanalysis of the bus-motor-failure data. Technometrics 37(4), 436-445 (1995). https://doi.org/10.1080/00401706.1995.10484372
[33] Nadarajah, S., Cordeiro, G.M., Ortega, E.M.: The exponentiated Weibull distribution: a survey. Stat. Pap. 54(3), 839-877 (2013). https://doi.org/10.1007/s00362-012-0449-x
[34] Nadarajah, S., Kotz, S.: The exponentiated type distributions. Acta Appl. Math. 92(2), 97-111 (2006). https://doi.org/10.1007/s10440-006-9062-0
[35] R Core Team.: R: a language and environment for statistical computing. R Foundation for Statistical Computing. https://www.R-project.org/ (2018)
[36] Silva, R., Gomes-Silva, F., Ramos, M., Cordeiro, G.M., Marinho, P., De Andrade, T.A.: The exponentiated Kumaraswamy-G class: general properties and application. Revista Colombiana de Estadística 42(1), 1-33 (2019). https://doi.org/10.15446/rce.v42n1.66205
[37] Vidovi, Z., Nikoli, J., Peri, Z.: Properties of k-record posteriors for the Weibull model. Statistical Theory and Related Fields 8(2), 152-162 (2024). https://doi.org/10.1080/24754269.2024.2322312
[38] Zelterman, D.: Parameter estimation in the generalized logistic distribution. Computational Statistics & Data Analysis 5(3), 177-184 (1987)

The Three-Parameter Exponentiated Weibull Exponential Distribution: Theoretical Properties and Practical Implications

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