10.57647/mathsci.2026.85781

An Improved Extension of Unit Moment Exponential Distribution: Mathematics, Inference, and Applications

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  • Bayan Adel Shukr*1,
  1. Department of Management Information Systems, College of Business Administration, Taibah University, Janadah Bin Umayyah Road, Tayba, Madinah 42353, Saudi Arabia

Received: 2025-11-27

Revised: 2025-12-20

Accepted: 2025-12-25

Published in Issue 2026-03-31

Published Online: 2026-03-15

Copyright (c) 2026 Bayan Adel Shukr (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Shukr, B. A. (2026). An Improved Extension of Unit Moment Exponential Distribution: Mathematics, Inference, and Applications . Mathematical Sciences, 20(1). https://doi.org/10.57647/mathsci.2026.85781
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Abstract

This study contributes to the derivation of a bounded probability model for unit interval data analysis. The proposed model is named the Sine Unit Moment Exponential (SUME) distribution. This SUME model has the potential to model both the monotone increase and the bathtub shape for the hazard function. We investigate various statistical properties, including mixture representation, moments, quantile function, mean residual life function, and order statistics. The parameter estimation of the SUME distribution is discussed using six different estimation approaches. A comprehensive simulation study is performed to assess frequentist properties of the considered estimation methodologies. Two different datasets related to failure time and milk production are utilized to evaluate the practicality and flexibility of the proposed distribution over renowned unit interval distributions.

Keywords

  • Unit ME distribution,
  • Sine-G family,
  • Moments,
  • Inference,
  • Failure time,
  • Milk production data
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References

  1. Abd El-Bar, A. M. T., El-Saeed, A. R., & Gemeay, A. M. (2025). A bounded Lindley exponential model with applications to industrial engineering and epidemiological data. AIMS MATHEMATICS, 10(7), 16233–16263.
  2. Ahmad, A., Rather, A. A., Tashkandy, Y. A., Bakr, M. E., Mohie El-Din, M. M., Gemeay, A. M., Almetwally, E. M., & Salem, M. (2024). Deriving the new cotangent Fréchet distribution with real data analysis. Alexandria Engineering Journal, 105(July), 12–24. https://doi.org/10.1016/j.aej.2024.06.038
  3. Ahsan-ul-Haq, M., Farooq, M. U., Nagy, M., Mansi, A. H., Habineza, A., & Marzouk, W. (2024). A new flexible distribution: Statistical inference with application. AIP Advances, 14(3). https://doi.org/10.1063/5.0189404
  4. Ahsan-ul-Haq, M., Hashmi, S., Aidi, K., Ramos, P. L., & Louzada, F. (2020). Unit Modified Burr-III Distribution: Estimation, Characterizations and Validation Test. Annals of Data Science. https://doi.org/10.1007/s40745-020-00298-6
  5. Ahsan-ul-Haq, M., Memon, A. Z., & Chand, S. (2022). An Analysis of Generalized Exponential Uniform Distribution. Mathematical Problems in Engineering, 1–15. https://doi.org/10.1155/2022/6040943
  6. Alkhairy, I., Nagy, M., Muse, A. H., & Hussam, E. (2021). The Arctan- X Family of Distributions: Properties, Simulation, and Applications to Actuarial Sciences. Complexity, 2021. https://doi.org/10.1155/2021/4689010
  7. Alshammari, T. S., & Rashedi, K. A. (2025). Analysis of kidney patients and pump failure data using a new unit interval distribution. Alexandria Engineering Journal, 116, 374–384.
  8. Alzahrani, M. R., & Almohaimeed, M. (2025). Analysis, inference, and application of Unit Haq distribution to engineering data. Alexandria Engineering Journal, 117, 193–204.
  9. Anderson, T. W., & Darling, D. A. (1952). Asymptotic theory of certain" goodness of fit" criteria based on stochastic processes. The Annals of Mathematical Statistics, 23(2), 193–212.
  10. Bashiru, S. O., Isa, A. M., Khalaf, A. A., Khaleel, M. A., Arum, K. C., & Anioke, C. L. (2025). A hybrid cosine inverse Lomax-G family of distributions with applications in medical and engineering data. Nigerian Journal of Technological Development, 22(1), 261–278.
  11. Bashiru, S. O., Kayid, M., Mahmoud, R., Balogun, O. S., Abd El-Raouf, M. M., & Gemeay, A. M. (2025). Introducing the unit Zeghdoudi distribution as a novel statistical model for analyzing proportional data. Journal of Radiation Research and Applied Sciences, 18(1), 101204.
  12. Cheng, R. C. H., & Amin, N. A. K. (1983). Estimating parameters in continuous univariate distributions with a shifted origin. Journal of the Royal Statistical Society: Series B (Methodological), 45(3), 394–403. https://doi.org/https://doi.org/10.1111/j.2517-6161.1983.tb01268.x
  13. Choi, K., & Bulgren, W. G. (1968). An estimation procedure for mixtures of distributions. Journal of the Royal Statistical Society Series B: Statistical Methodology, 30(3), 444–460.
  14. Cordeiro, G. M., & dos Santos Brito, R. (2012). The beta power distribution. Brazilian Journal of Probability and Statistics, 26(1), 88–112. https://doi.org/10.1214/10-BJPS124
  15. Eliwa, M. S., Ahsan-Ul-Haq, M., Al-Bossly, A., & El-Morshedy, M. (2022). A Unit Probabilistic Model for Proportion and Asymmetric Data: Properties and Estimation Techniques with Application to Model Data from SC16 and P3 Algorithms. Mathematical Problems in Engineering, 2022, 1–13. https://doi.org/10.1155/2022/9289721
  16. Fletcher, R. (2000). Practical methods of optimization. John Wiley & Sons.
  17. Glänzel, W. (1987). A characterization theorem based on truncated moments and its application to some distribution families. In Mathematical statistics and probability theory (pp. 75–84). Springer.
  18. Hashmi, S., Ahsan-ul-Haq, M. A., Zafar, J., & Khaleel, M. A. (2022). Unit Xgamma Distribution: Its Properties, Estimation and Application. Proceedings of the Pakistan Academy of Sciences: Part A, 59(1), 15–28. https://doi.org/10.53560/PPASA(59-1)636
  19. Kharazmi, O., Alizadeh, M., Contreras-Reyes, J. E., & Haghbin, H. (2022). Arctan-based family of distributions: properties, survival regression, Bayesian analysis and applications. Axioms, 11(8), 399.
  20. Krishna, A., Maya, R., Chesneau, C., & Irshad, M. R. (2022). The unit Teissier distribution and its applications. Mathematical and Computational Applications, 27(1), 12.
  21. Kumar, D., Singh, U., & Singh, S. K. (2015). A new distribution using sine function-its application to bladder cancer patients data. Journal of Statistics Applications & Probability, 4(3), 417.
  22. Mahmood, Z., Chesneau, C., & Tahir, M. H. (2019). A new sine-G family of distributions: Properties and applications. Bulletin of Computational Applied Mathematics, 7(1), 53–81.
  23. Maya, R., Jodra, P., Irshad, M. R., & Krishna, A. (2024). The unit Muth distribution: Statistical properties and applications. Ricerche Di Matematica, 73(4), 1843–1866.
  24. Mazucheli, J., Menezes, A. F. B., & Dey, S. (2018). The unit-Birnbaum-Saunders distribution with applications. Chilean Journal of Statistics, 9(1), 47–57. http://www.soche.cl/chjs%0Ahttp://chjs.mat.utfsm.cl/volumes/09/01/Mazucheli_etal(2018).pdf
  25. Nanga, S., Nasiru, S., & Dioggban, J. (2023). Cosine Topp–Leone family of distributions: Properties and Regression. Research in Mathematics, 10(1). https://doi.org/10.1080/27684830.2023.2208935
  26. Nigm, A. M., Al-Hussaini, E. K., & Jaheen, Z. F. (2003). Bayesian one-sample prediction of future observations under Pareto distribution. Statistics, 37(6), 527–536.
  27. Odhah, O. H., Albalawi, O., & Alshanbari, H. M. (2025). A new trigonometric-oriented distributional method: Model, theory, and practical applications. Alexandria Engineering Journal, 120(January), 1–12. https://doi.org/10.1016/j.aej.2025.01.096
  28. Rajkumar, J., & Sakthivel, K. M. (2022). A New Method of Generating Marshall–Olkin Sine–G Family and Its Applications in Survival Analysis. Lobachevskii Journal of Mathematics, 43(2), 463–472. https://doi.org/10.1134/S1995080222050213
  29. Sindhu, T. N., Shafiq, A., Riaz, M. B., Abushal, T. A., Ahmad, H., Almetwally, E. M., & Askar, S. (2024). Introducing the new arcsine-generator distribution family: An in-depth exploration with an illustrative example of the inverse weibull distribution for analyzing healthcare industry data. Journal of Radiation Research and Applied Sciences, 17(2), 100879. https://doi.org/10.1016/j.jrras.2024.100879
  30. Swain, J. J., Venkatraman, S., & Wilson, J. R. (1988). Least-squares estimation of distribution functions in Johnson’s translation system. Journal of Statistical Computation and Simulation, 29(4), 271–297.
  31. Tahir, M. H., & Nadarajah, S. (2015). Parameter induction in continuous univariate distributions: Well-established G families. Anais Da Academia Brasileira de Ciências, 87(2), 539–568.
  32. Tomy, L., & Dominic, L. (2024). Review on Distributions Generated Using Trigonometric Functions. Austrian Journal of Statistics, 53(3), 102–119. https://doi.org/10.17713/ajs.v53i3.1827