Log-generalized exponential-Poisson regression model and its application to real data
DOI:
https://doi.org/10.64497/jssci.171Keywords:
Generalized exponential Poisson distribution, log-linear regression models, simulation, residual analysis, maximum likelihood estimationAbstract
In this paper, we propose a log-generalized exponential Poisson (LGEP) regression model based on generalized exponential Poisson distribution, and some of its structural properties are derived, including distribution function, density function, quantile function, and survival function. Secondly, we developed maximum likelihood estimation (MLE) for the model parameters estimation, also, performed some simulation analysis for different parameter settings and sample sizes to evaluate the performance of the MLEs by analyzing the mean squared error of the MLEs. Finally, we use two set of experimental data, one on the anesthesia response of guinea pigs, and the second on the percentage body fat in human to examine the performance of the LGEP regression model. The results show that the LGEP regression model provides more reliable results and has a better fit than the log-exponential Poisson, log-generalize exponential, and log-generalize extended exponential regression models. In the first data the proposed model reveals that the dosage of the anesthetic drug was shown to exert a positive effect on guinea pigs sleep duration once it reached an adequate level; also, for the second data, the proposed model suggests that both gender and BMI positively influence the percentage body fat across the subjects.
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[1]M. P. Allen, Understanding regression analysis, Springer Science & Business Media, 2004.
[2]Fahrmeir, Ludwig, et al. "Regression models." Regression: Models, methods and applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 2022. 23-84. DOI: https://doi.org/10.1007/978-3-662-63882-8_2
[3] Muhammad M, Sallam Salem Abdalla G, Faal A, Almetwally EM, Elgarhy M. A Flexible Approach to Quantile Regression Modeling With Unit Burr‐XII‐Poisson and Its Applications to Cancer, Chemotherapy, and Energy Data. Engineering Reports. 2025;7(8):e70312. DOI: https://doi.org/10.1002/eng2.70312
[4] Muhammad M, Abba B, Xiao J, Alsadat N, Jamal F, Elgarhy M. A new three-parameter flexible unit distribution and its quantile regression model. IEEE Access. 2024;23. DOI: https://doi.org/10.1109/ACCESS.2024.3485219
[5] Muhammad M. A new three-parameter model with support on a bounded domain: Properties and quantile regression model. Journal of Computational Mathematics and Data Science. 2023 Jan 1;6:100077. DOI: https://doi.org/10.1016/j.jcmds.2023.100077
[6]Muse AH, Ngesa O, Mwalili S, Alshanbari HM, El-Bagoury AA. A Flexible Bayesian Parametric Proportional Hazard Model: Simulation and Applications to Right‐Censored Healthcare Data. Journal of Healthcare Engineering. 2022;2022(1):2051642. DOI: https://doi.org/10.1155/2022/2051642
[7]Sadiq, I. A., Kajuru, J. Y., Doguwa, S. I., Yahaya, S. S., Gambo, Y. Y., Hephzibah, A. A., … Bello, A. (2025). Survival analysis in advanced lung cancer using Weibull survival regression model: estimation, interpretation, and clinical application. Journal of Statistical Sciences and Computational Intelligence, 1(2), 106–123. DOI: https://doi.org/10.64497/jssci.30
[8]Panitanarak, U., Ishaq, A. I., Usman, A., Sadiq, I. A., & Mohammed, A. S. (2025). The modified sine distribution and machine learning models for enhancing crude oil production prediction. Journal of Statistical Sciences and Computational Intelligence, 1(1), 29–45 DOI: https://doi.org/10.64497/jssci.3
[9]Muhammad, M., Abba, B., Muhammad, I., Bakouch, H. S., & Xiao, J. (2025). A versatile family of distributions: Log-linear regression model and applications to real data. Kuwait Journal of Science, 52(2), 100385. DOI: https://doi.org/10.1016/j.kjs.2025.100385
[10] Altun, E. (2021). The log-weighted exponential regression model: alternative to the beta regression model. Communications in Statistics-Theory and Methods, 50(10), 2306-2321. DOI: https://doi.org/10.1080/03610926.2019.1664586
[11] Arasan, J., & Midi, H. (2024). Modified outlier diagnostics for the extended exponential regression model with interval and right-censored data. Communications in Statistics - Theory and Methods, 54(7), 1991–2004. DOI: https://doi.org/10.1080/03610926.2024.2354814
[12]Klakattawi, H.S. A Novel Exponentiated Generalized Weibull Exponential Distribution: Properties, Estimation, and Regression Model. Axioms 2025, 14, 706. DOI: https://doi.org/10.3390/axioms14090706
[13]Dawlah, Alsulami, and Amani S. Alghamdi. "A New Extended Weibull Distribution: Estimation Methods and Applications in Engineering, Physics, and Medicine." Mathematics 13.20 (2025): 3262. DOI: https://doi.org/10.3390/math13203262
[14]Anafo, Abdulzeid Yen, Ocloo, Selasi Kwaku, Nasiru, Suleman, New Weighted Burr XII Distribution: Statistical Properties, Applications, and Regression, International Journal of Mathematics and Mathematical Sciences, 2024(14), 4098771. DOI: https://doi.org/10.1155/2024/4098771
[15] Alghamdi, A.S.; ALoufi, S.F.; Baharith, L.A. The Sine Alpha Power-G Family of Distributions: Characterizations, Regression Modeling, and Applications. Symmetry 2025, 17, 468. DOI: https://doi.org/10.3390/sym17030468
[16] E. Hussam, R. A. Aldallal, L. Prasad Sapkota, and A. M. Gemeay, “ A Modified Half-Logistic Distribution With Regression Analysis,” Engineering Reports 7( 11), 2025: e70487 DOI: https://doi.org/10.1002/eng2.70487
[17] Risti´c MM, Nadarajah S. A new lifetime distribution. Journal of Statistical Computation and Simulation 2012. DOI:10.1080/00949655.2012.697163 DOI: https://doi.org/10.1080/00949655.2012.697163
[18]Renwang Liao, Kaihong Dong, Mustapha Muhammad, Jinsen Xiao. Log-generalized extended exponential (LGEE) regression model and it application to dielectrics breakdown strength data. Advances and Applications in Statistics.2023 (Accepted manuscript)
[19]Bailey R, Summe J, Homer L, et al. A Model for Analysis of the Anesthetic Response. Biometrics, 1978. 223-32. DOI: https://doi.org/10.2307/2530012
[20] R. B. Mazess, W. W. Peppler, and M. Gibbons. Total body composition by dualphoton (153Gd) absorptiometry. American Journal of Clinical Nutrition,1984. 40, 834–839. DOI: https://doi.org/10.1093/ajcn/40.4.834
[21] D. J. Hand, F. Daly, A. D. Lunn, K. J. McConway, and E. Ostrowski (1994) A Handbook of Small Data Sets, London: Chapman and Hall. Dataset 17. DOI: https://doi.org/10.1007/978-1-4899-7266-8
[22]Dunn PK, Smyth GK. GLMsData: generalized linear model data sets. R package version. 2018.
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Copyright (c) 2026 Kaihong Dong, Renwang Liao, Mustapha Muhammad , Jinsen Xiao
This work is licensed under a Creative Commons Attribution 4.0 International License.
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