Extension of the heavy-tailed distribution with applications in medical sciences

Chamunorwa, Simbarashe; Oluyede, Broderick; Chipepa, Fastel; Ranonna, Kethamile

doi:10.47974/JSMS-1358

Open Access Research Article

Extension of the heavy-tailed distribution with applications in medical sciences

^*Simbarashe ChamunorwaCorresponding authorCS19100117@biust.ac.bw simbarashe.chamunorwa@staff.msuas.ac.zwAffiliation 1Department of Mathematics and Statistical SciencesBotswana International University of Science and TechnologyPalapye, BotswanaAffiliation 2Department of Applied StatisticsManicaland State University of Applied SciencesMutare, ZimbabweView full profile → , Broderick Oluyedeoluyedeo@biust.ac.bwDepartment of Mathematics and Statistical SciencesBotswana International University of Science and TechnologyPalapye, BotswanaView full profile → , Fastel Chipepachipepaf@biust.ac.bwDepartment of Mathematics and Statistical SciencesBotswana International University of Science and TechnologyPalapye, BotswanaView full profile → , Kethamile RanonnaRK15000146@biust.ac.bwDepartment of Mathematics and Statistical SciencesBotswana International University of Science and TechnologyPalapye, BotswanaView full profile →

* Corresponding author · click or hover a name for details

pp. 111–133Vol. 29Issue 2February 2026DOI: 10.47974/JSMS-1358XML

Received:: 09 Jan 2024
Published Online:: 30 Oct 2025
Article type:: Research Article
Language:: EN
Article no.:: JSMS-1358
Pages:: 111–133

Abstract

Heavy-tailed-Type II Exponentiated Half Logistic-Gompertz-G (HT-TIIExHL-G-G) class of distributions is proposed in this article. The structural properties of the distribution are thoroughly explored, and specific cases within this family are presented. We carried out simulation study to explore the estimation of the model parameters through several established techniques. The analysis showcased their numerical efficiency and performance. Furthermore, through the utilization of maximum likelihood technique, we use a specific instance from the HT-TIIExHL-G-G family of distributions (FD) to show its practical application. This is achieved by fitting it to three real-world data examples from health care and engineering disciplines.

Keywords

Heavy-tailed distribution Exponentiated distribution Gompertz distribution Simulations Maximum likelihood estimation

Subject Classifications

60E0562E1562F30

References

[1] A. Algarni, A. M. Almarashi, I. Elbatal, M. A. Hassan, E. Almetwally, A. Daghistani, and M. Elgarhy, “Type I Half Logistic Burr X-G Family: Properties, Bayesian, and Non Bayesian Estimation Under Censored Samples and Applications to COVID-19 Data,” Mathematical Problems in Engineering, vol. 2021, pp. 1–21 (2021), doi: 10.1155/2021/5461130.
[2] M. Alizadeh, G. M. Cordeiro, G. Pinho, and I. Ghosh, “The Gompertz-G Family of Distributions,” Journal of Statistical Theory and Practice, vol. 11, no. 1, pp. 179–207 (2017).
[3] S. Chamunorwa, B. Oluyede, T. Moakofi, and F. Chipepa, “The Type II Exponentiated Half Logistic-Gompertz-G Power Series Class of Distributions: Properties and Applications,” Statistics, Optimization & Information Computing, vol. 12, no. 2, pp. 381–399 (2024), doi: 10.19139/soic-2310-5070-1721.
[4] G. Chen and N. Balakrishnan, “A General Purpose Approximate Goodness-of-Fit Test,” Journal of Quality Technology, vol. 27, no. 2, pp. 154–161 (1985).
[5] K. Dutta and J. Perry, “A Tale of Tails: An Empirical Analysis of Loss Distribution Models for Estimating Operational Risk Capital,” (2006). [Online]. Available: (Add URL if available).
[6] B. Gompertz, “On the Nature of the Function Expressive of the Law of Human Mortality and on the New Mode of Determining the Value of Life Contingencies,” Philosophical Transactions of the Royal Society of London, vol. 115, pp. 513–580 (1825).
[7] S. Harini, M. Subbiah, and M. R. Srinivasan, “Fitting Length of Stay in Hospitals Using Transformed Distributions,” Communications in Statistics: Case Studies, Data Analysis and Applications, vol. 4, no. 1, pp. 1–8 (2017).
[8] A. Ickowicz and R. Sparks, “Modelling Hospital Length of Stay Using Convolutive Mixtures Distributions,” Statistics in Medicine, vol. 36, no. 1, pp. 122–135 (2017), doi: 10.1002/sim.7148. PMID: 27704639.
[9] B. Oluyede, S. Chamunorwa, F. Chipepa, and M. Alizadeh, “The Topp-Leone-Gompertz-G Family of Distributions with Applications,” Journal of Statistics and Management Systems, vol. 25, no. 6, pp. 1399–1423 (2021), doi: 10.1080/09720510.2021.1972623.
[10] B. Oluyede and T. Moakofi, “Type II Exponentiated Half-Logistic-Gompertz-Topp-Leone-G Family of Distributions with Applications,” Central European Journal of Economic Modelling and Econometrics, vol. 14, pp. 415–461 (2022).
[11] K. Rannona, B. Oluyede, and S. Chamunorwa, “The Gompertz-Topp Leone-G Family of Distributions with Applications,” Journal of Probability and Statistical Science, vol. 20, no. 1, pp. 108–126 (2022).
[12] C. E. Shannon, “Prediction and Entropy of Printed English,” The Bell System Technical Journal, vol. 30, pp. 50–64 (1951).
[13] J. Zendehdel, R. Zarei, and S. M. Mahmoudi, “A New Generalized Weibull-Gompertz Distribution and Its Properties,” Journal of Statistics and Management Systems, vol. 25, no. 4, pp. 837–856 (2022), doi: 10.1080/09720510.2021.1938997.
[14] J. Zhao, Z. Ahmad, E. Mahmoudi, E. Hossam, and M. M. M. El-Din, “A New Class of Heavy-Tailed Distributions: Modelling and Simulating Actuarial Measures,” Complexity, pp. 1–18 (2021), doi: 10.1155/2021/5580228.
[15] W. Zhao, S. K. Khosa, Z. Ahmad, M. Aslam, and A. Z. Afify, “Type-I Heavy-Tailed Family with Applications in Medicine, Engineering and Insurance,” PLoS ONE, vol. 15, no. 8, e0237462 (2020), doi: 10.1371/journal.pone.0237462.

Views: 143Downloads: 69Citations: 0