10.57647/mathsci.2025.1904.18008

Transmuted One-parameter Sarhan-Tadj-Hamilton Distribution: Properties and Applications

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  • F.A. Shiha*1,
  • Abdulrahman M. A. Aldawsari2,
  • Reid Alotaibi3,
  • Alia M. Magar1,
  1. Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt
  2. Department of Mathematics, College of Sciences and Humanities, Prince Sattam Bin Abdulaziz University, Al-Kharj 16273, Saudi Arabia
  3. Department of Mathematics, College of Science and Humanities, Shaqra University, Shaqra, Saudi Arabia

Received: 2025-09-06

Revised: 2025-10-21

Accepted: 2025-10-27

Published in Issue 2026-03-31

Published Online: 2025-11-16

Copyright (c) 2026 Faten Shiha, Abdulrahman M. A. Aldawsari, Reid Alotaibi, Alia M. Magar (Author)

Creative Commons License

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

How to Cite

Shiha, F., Aldawsari, A. M. A., Alotaibi, R., & Magar, A. M. (2026). Transmuted One-parameter Sarhan-Tadj-Hamilton Distribution: Properties and Applications. Mathematical Sciences, 20(1). https://doi.org/10.57647/mathsci.2025.1904.18008
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Abstract

Transmuted distributions have gained attention in statistical modeling due to their flexibility and ability to enhance the performance of baseline distributions. In this article, we introduce the transmuted one-parameter Sarhan-Tadj-Hamilton distribution. Various structural properties of the proposed distribution, such as explicit expressions, stochastic orders, moments, and order statistics are derived. Six  parameter estimation methods are examined, with their relative performance compared through Monte Carlo simulations and ranked  across different sample sizes. The proposed model is further validated using multiple real data sets, demonstrating its practical flexibility.

Keywords

  • Transmuted distribution,
  • Skewed distribution,
  • Estimation,
  • Simulation,
  • Goodness of fit
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References

  1. M. Ahsan-ul-Haq, Transmuted exponentiated inverse rayleigh distribution, Journal of statistics applications and probability, 5(2) (2016), 337–343
  2. M. Ahsan-ul-Haq, A.Z. Memon, S. Chand, An analysis of generalized exponential uniform distribution, Math. Probl. Eng., (2022), 1—15 (2022), https://doi.org/10.1155/ 2022/604094
  3. M. Ahsan-ul-Haq, M. U. Farooq, M. Nagy, A. H. Mansi, A. Habineza, W. Marzouk, A new flexible distribution: Statistical inference with application, AIP Advances, 14, 035030 (2024). https://doi.org/10.1063/5.018940
  4. M. Z. Arshad, M. Z. Iqbal, A. Al Mutairi, A comprehensive review of datasets for statistical research in probability and quality control, J. Math. Comput. Sci., 11 (2021), 3663–3728. [5] H. M. Alshanbari, O. H. Odhah, H. Al-Mofleh, Z. Ahmad, S. K. Khosa, and A. A. H. El-Bagoury, A new flexible Weibull extension model: Different estimation methods and modeling an extreme value data, Heliyon, 9(11) (2023) e21704. doi: 10.1016/j.heliyon.2023.e21704, PMID: 38027837 PMCID: PMC10665740
  5. B. C. Arnold, N. Balakrishnan, and H. N. Nagaraja, A first course in order statistics. New York: Wiley, 1992
  6. A. Azzalini, A class of distributions which includes the normal ones, Scand. J. Stat., 12 (1985), 171–178
  7. N. Balakrishnan, and M. M. Risti´c, Multivariate families of gamma-generated distributions with finite or infinite support above or below the diagonal, J. Multivariate Anal., 143 (2016), 194–207
  8. H. M. Barakat, A new method for adding two parameters to a family of distributions with application to the normal and exponential families, Stat. Methods Appl., 24 (2015) 359–372
  9. D. H. Barlow, A.S. Cohen, M.T. Waddell, B.B. Vermilyea, J.S. Klosko, E.B. Blanchard, P.A. Di Nardo, Panic and generalized anxiety disorders: Nature and treatment, Behav. Therapy. 15 (1984), 431–449
  10. D. K. Bhaumik, K. Kapur, R.D. Gibbons, Testing parameters of a gamma distribution for small samples, Technometrics, 51(3) (2009), 326–334.
  11. S. Dey, D. Kumar, M.Z. Anis, N. Saralees, and O. Idika. A review of transmuted distributions. J. Indian Soc. Probab. Stat., 22 (2021), 47–111. https://doi.org/10.1007/s41096-021-00096-0
  12. N. Eugene, C. Lee, and F. Famoye, Beta-normal distribution and its applications, Communications in Statistics-Theory and Methods, 31(4) (2002) , 497–512.
  13. M. Gharaibieh, Transmuted Aradhana distribution: properties and application, Jordan Journal of Mathematics and Statistics, 13 (2020), 287–304.
  14. E. A.A.Hassan, M.Elgarhy, E.A. Eldessouky, O.H.M. Hassan, E.A. Amin, and E.M. Almetwally, Different estimation methods for new probability distribution approach based on environmental and medical data. Axioms, 12 (2023), 220. https://doi.org/10.3390/axioms12020220
  15. D. V. Lindley, Fiducial distributions and Bayes’ theorem, Journal of the Royal Statistical Society, Series B, 20 (1958), 102–107.
  16. A. W. Marshall, and I. Olkin, A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika, 84(3) (1997), 641–652.
  17. G. S. Mudholkar, and D. K. Srivastava, Exponentiated Weibull family for analyzing bathtub failure-rate data, IEEE Trans. Reliab., 42(2) (1993), 299–302.
  18. G. S. Mudholkar, A. D. Hutson, The exponentiated Weibull family: some properties and a flood data application, Commun Stat-Theory Methods, 25 (1996), 3059—3083.
  19. D. N. P. Murthy, M. Xie, and R. Jiang, Weibull Models, John Wiley & Sons Inc., Hoboken, NJ., 2004.
  20. R. D. Gupta, and D. Kundu, Theory and methods: Generalized exponential distributions, Australian and New Zealand Journal of Statistics, 41(2) (1999), 173–188.
  21. M. A. Hussian, Transmuted exponentiated gamma distribution: a generalization of the exponentiated gamma probability distribution, Appl. Math. Sci., 8 (2014), 1297–1310.
  22. M. S. Khan, and R. King, Transmuted modified Weibull distribution: A generalization of the modified Weibull probability distribution, Eur. J. Pure Appl. Math., 6 (2013), 66–88
  23. F. Merovci, Transmuted Rayleigh distribution, Austrian J. Stat., 42(1) (2013), 21–31
  24. A. M. Sarhan, L. Tadj, and D. C. Hamilton, A new lifetime distribution and its power transformation, J. Probab. Stat., 2014 (2014), 1–14. doi:10.1155/2014/53202
  25. S. Sen, S. S. Maiti, and N. Chandra, The xgamma distribution: Statistical properties and application, Journal of Modern Applied Statistical Methods.15(1) (2016), Article 38. DOI: 10.22237/jmasm/146207742
  26. M. Shaked and J. G. Shanthikumar, Stochastic Orders, Wiley, New York 2007
  27. W. T. Shaw, and I. R. Buckley, The alchemy of probability distributions: beyond Gram- Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map, (2009). https://arxiv.org/abs/0901.043
  28. M. K. Thame, and R. Zine, Comparison of five methods to estimate the parameters for the three-parameter lindley distribution with application to life data, Comput. Math. Methods Med., 2021 , Article ID 2689000