The Weibull Exponential {Logistic} Poisson Distribution: Properties and Application
DOI:
https://doi.org/10.33003/fjs-2026-1019-6043Keywords:
Weibull Exponential {Logistic} Poisson Distribution, Maximum Likelihood Estimation, Lifetime Data, Goodness-of-Fit, Hazard FunctionAbstract
This paper introduces the Weibull Exponential {Logistic} Poisson Distribution (WELPD), a new five-parameter lifetime distribution obtained by compounding the Weibull Exponential {Logistic} distribution of (Eno et al., 2022) with the power series family of distributions proposed by (Osatohanmwen et al., 2020). The probability density function, cumulative distribution function, survival function, and hazard function are derived. Comprehensive statistical properties including the quantile function, moments, moment generating function, skewness, and kurtosis are investigated. The parameters are estimated using the method of maximum likelihood. The flexibility and superiority of the proposed distribution are demonstrated through application to real life data of the failure times of electric bulbs dataset. The results indicate that the WELPD provides a better fit compared to the Weibull Exponential {Logistic} Distribution (WELD) and the Weibull Logistic Distribution (WLD), as evidenced by lower values of the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Kolmogorov-Smirnov (K-S) statistic, Cramér-von Mises (CM) statistic, and Anderson-Darling (AD) statistic.
References
Alzaatreh, A., & Ghosh, I. (2015). On the Weibull-X family of distributions. Journal of statistical theory and applications, 14(2), 169-183.
Akarawak, E. E., Adeleke, I., Olalude, G. A., & Ekum, M. I. (2021). The Four-Parameter Weibull-Logistic Distribution: Properties and Application. Available at SSRN 3971598.
Osatohanmwen, P., Oyegue, F. O., & Ogbonmwan, S. M. (2020). The T–R {Y} power series family of probability distributions. Journal of the Egyptian Mathematical Society, 28(1), 29.
Shanker, R. (2023). Komal distribution with properties and application in survival analysis. Biometrics & Biostatistics International Journal, 12(2), 40-44.
Shukla, K. K. (2019). A comparative study of one parameter lifetime distributions. Biometrics & Biostatistics International Journal, 8(4), 111-123.
Hashem, A. F., Abdelkawy, M. A., Muse, A. H., & Yousof, H. M. (2024). A novel generalized Weibull Poisson-G class of continuous probabilistic distributions with some copulas, properties and applications to real-life datasets. Scientific Reports, 14, 1741. https://doi.org/10.1038/s41598-023-49873-w
Klakattawi, H. S. (2025). A novel exponentiated generalized Weibull exponential distribution: Properties, estimation, and regression model. Axioms, 14(9), 706. https://doi.org/10.3390/axioms14090706
Adamidis, K., & Loukas, S. (1998). A lifetime distribution with decreasing failure
rate. Statistics & Probability Letters, 39(1), 35-42.
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Copyright (c) 2026 Rufai Iliyasu, Kazeem Eyitayo Lasisi, Abubakar Bishir, Ishaq Abdullahi Baba, Jamilu Yunusa Falgore, Mannir Abdu, Salihu Gambo, Shehu Abba Adamu
This work is licensed under a Creative Commons Attribution 4.0 International License.
