Pandawa Logo

Scopus CiteScore 2024

4.8

Calculated on 05 May, 2025

SJR 2024

0.31

Powered by scimagojr.com

Language

Journal of Multidisciplinary Applied Natural Science

ISSN (eletronic): 2774-3047


Vol. 6 Issue 1 (2026) Articles https://doi.org/10.47352/jmans.2774-3047.306

Truncated Transmuted Exponential Distribution with Different Estimation Methods and Applications

Ahmed Mohamed El Gazar Diaa S Metwally Mohammed Elgarhy Beih S El-Desouky

Author information

Ahmed Mohamed El Gazar

https://orcid.org/0009-0008-5040-8924
  • ahmedaljazzar@hics.edu.eg
  • Department of Basic Sciences, Higher Institute for Commercial Sciences, Almahlla Alkubra-31951 (Egypt)
  • Biography not informed.

Author information

Diaa S Metwally

https://orcid.org/0009-0005-8319-1520
  • dmetwally@imamu.edu.sa
  • Deanship of Scientific Research, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh-11432 (Saudi Arabia)
  • Biography not informed.

Author information

Mohammed Elgarhy

https://orcid.org/0000-0002-1333-3862
  • dr.moelgarhy@gmail.com
  • Department of Basic Sciences, Higher Institute of Administrative Sciences, AlSharkia-1841104 (Egypt)
  • Biography not informed.

Author information

Beih S El-Desouky

https://orcid.org/0000-0002-1330-464X
  • b_desouky@yahoo.com
  • Department of Mathematics, Mansoura University, Mansoura-35516 (Egypt)
  • Biography not informed.

Published in: September 24, 2025

[1]
A. M. El Gazar, D. S. Metwally, M. Elgarhy, and B. S. El-Desouky, “Truncated Transmuted Exponential Distribution with Different Estimation Methods and Applications”, J. Multidiscip. Appl. Nat. Sci., vol. 6, no. 1, pp. 19–43, Sep. 2025.

Abstract

In this study, we study and discuss a new truncated flexible distribution named the truncated transmuted exponential distribution. The probability density function of the new suggested model is decreasing, but its hazard rate function is increasing. Some fundamental statistical properties of the new distribution are computed such as moments, incomplete moments, moment generating function, quantile function, mean residual lifetime, mean past lifetime, order statistics, and extropy. Various approaches of estimation are considered include maximum likelihood, least squares, weighted least squares, Cramér-Von-Mises, maximum product of spacings, Anderson-Darling, right-tail Anderson-Darling and percentile methods. A simulation study is established to assess the accuracy of estimates through some measures.  The importance of the truncated transmuted exponential model is demonstrated using real lifetime data, and its goodness-of-fit is evaluated against alternative models. This study offers a more accurate match to the data compared to other competing models.

References

  • [1] W. T. Shaw and I. R. Buckley. (2007). "The alchemy of probability distributions: beyond GramCharlier expansions and a skew kurtostic-normal distribution from a rank transmutation map". Research report.  

  • [2] F. Merovci. (2016). "Transmuted Rayleigh Distribution". Austrian Journal of Statistics. 42 (1): 21-31. 10.17713/ajs.v42i1.163.

    DOI: https://doi.org/10.17713/ajs.v42i1.163
  • [3] M. S. Khan and R. King. (2013). "Transmuted modified Weibull distribution: A Generalization of the Modified Weibull Probability Distribution". European Journal of Pure and Applied Mathematics. 6 : 66-88.

  • [4] M. S. Khan, R. King, and I. Hudson. (2014). "Characterizations of the transmuted inverse Weibull distribution". ANZIAM Journal. 54. 10.21914/anziamj.v55i0.7785.

    DOI: https://doi.org/10.21914/anziamj.v55i0.7785
  • [5] F. Samuel Adeyinka. (2019). "On Transmuted Four Parameters Generalized Log-Logistic Distribution". International Journal of Statistical Distributions and Applications. 5 (2). 10.11648/j.ijsd.20190502.12.

    DOI: https://doi.org/10.11648/j.ijsd.20190502.12
  • [6] F. Merovci and L. Puka. (2014). "Transmuted Pareto distribution". ProbStat Forum. 7 1-11.

  • [7] M. Ahsan-Ul-Haq, M. A. Aldahlan, J. Zafar, H. W. Gomez, A. Z. Afify, and H. A. Mahran. (2023). "A new cubic transmuted power-function distribution: Properties, inference, and applications". PLoS One. 18 (2): e0281419. 10.1371/journal.pone.0281419.

    DOI: https://doi.org/10.1371/journal.pone.0281419
  • [8] A. F. Samuel. (2019). "On the Performance of Transmuted Logistic Distribution: Statistical Properties and Application". Budapest International Research in Exact Sciences (BirEx) Journal. 1 (3): 34-42. 10.33258/birex.v1i3.341.

    DOI: https://doi.org/10.33258/birex.v1i3.341
  • [9] S. Naz, L. A. Al-Essa, H. S. Bakouch, and C. Chesneau. (2023). "A Transmuted Modified Power-Generated Family of Distributions with Practice on Submodels in Insurance and Reliability". Symmetry. 15 (7):  10.3390/sym15071458.

    DOI: https://doi.org/10.3390/sym15071458
  • [10] A. Ahmad, M. Jallal, S. Q. Ain, and R. Tripathi. (2021). "Burhan Distribution with Structural Properties and Applications in Distinct Areas of Science". Earthline Journal of Mathematical Sciences. 429-445. 10.34198/ejms.7221.429445.

    DOI: https://doi.org/10.34198/ejms.7221.429445
  • [11] G. R. Aryal and C. P. Tsokos. (2009). "On the transmuted extreme value distribution with application". Nonlinear Analysis: Theory, Methods & Applications. 71 (12): e1401-e1407. 10.1016/j.na.2009.01.168.

    DOI: https://doi.org/10.1016/j.na.2009.01.168
  • [12] G. R. Aryal and C. P. Tsokos. (2011). "Transmuted Weibull distribution: A Generalization of the Weibull Probability Distribution". European Journal of Pure and Apllied Mathematics. 4 (2): 89-102.

  • [13] E. A. Eldessouky, O. H. M. Hassan, B. Aloraini, and I. Elbatal. (2025). "Modeling to medical and economic data using: The transmuted power unit inverse Lindley distribution". Alexandria Engineering Journal. 113 : 633-647. 10.1016/j.aej.2024.11.008.

    DOI: https://doi.org/10.1016/j.aej.2024.11.008
  • [14] M. M. Badr, I. Elbatal, F. Jamal, C. Chesneau, and M. Elgarhy. (2020). "The Transmuted Odd Fréchet-G Family of Distributions: Theory and Applications". Mathematics. 8 (6). 10.3390/math8060958.

    DOI: https://doi.org/10.3390/math8060958
  • [15] M. Elgarhy, I. Elbatal, M. A. ul Haq, and A. S. Hassan. (2018). "Transmuted Kumaraswamy Quasi Lindley Distribution with Applications". Annals of Data Science. 5 (4): 565-581. 10.1007/s40745-018-0153-4.

    DOI: https://doi.org/10.1007/s40745-018-0153-4
  • [16] M. Elgarhy, V. K. Sharma, and I. Elbatal. (2018). "Transmuted Kumaraswamy Lindley distribution with application". Journal of Statistics and Management Systems. 21 (6): 1083-1104. 10.1080/09720510.2018.1481003.

    DOI: https://doi.org/10.1080/09720510.2018.1481003
  • [17] S. K. Sinha.(1986)." Reliability and Life Testing". Wiley Estern Limited, New Delhi.

  • [18] S. E. Ahmed, C. Castro-Kuriss, E. Flores, V. Leiva, and A. Sanhueza. (2010). "A truncated version of the birnbaum-saunders distribution with an application in financial risk". Pakistan Journal of Statistics. 26 : 293-311.

  • [19] I. B. Aban, M. M. Meerschaert, and A. K. Panorska. (2006). "Parameter Estimation for the Truncated Pareto Distribution". Journal of the American Statistical Association. 101 (473): 270-277. 10.1198/016214505000000411.

    DOI: https://doi.org/10.1198/016214505000000411
  • [20] L. Zaninetti and M. Ferraro. (2008). "On the truncated Pareto distribution with applications". Open Physics. 6 (1): 1-6. 10.2478/s11534-008-0008-2.

    DOI: https://doi.org/10.2478/s11534-008-0008-2
  • [21] D. P. Murthy, M. R. Xie, and J. Jiang.(2004)." Weibull Models". John Wiley and Sons.

  • [22] T. Zhang and M. Xie. (2011). "On the upper truncated Weibull distribution and its reliability implications". Reliability Engineering & System Safety. 96 (1): 194-200. 10.1016/j.ress.2010.09.004.

    DOI: https://doi.org/10.1016/j.ress.2010.09.004
  • [23] A. M. Elgazar, M. Elgarhy, and B. S. El-Desouky. (2022). "Truncated moment exponentail distribution with application". Journal of Neuroquantology. 20 (14): 946-958.

  • [24] H. M. Hussein and M. T. Ahmed. (2021). "Family of [0,1] truncated Gompertz - exponential distribution with properties and application". Turkish Journal of Computer and Mathematics Education. 12 (14): 1383-1399.

  • [25] A. M. Almarashi, F. Jamal, C. Chesneau, M. Elgarhy, and Y. Su. (2021). "A New Truncated Muth Generated Family of Distributions with Applications". Complexity. 2021 (1). 10.1155/2021/1211526.

    DOI: https://doi.org/10.1155/2021/1211526
  • [26] N. Elah, P. B. Ahmad, and M. A. Wani. (2023). "A new zero-truncated distribution and its applications to count data". Reliability: Theory & Applications. 18 (2): 327-339.

  • [27] A. M. El Gazar, M. ElGarhy, and B. S. El-Desouky. (2023). "Classical and Bayesian estimation for the truncated inverse power Ailamujia distribution with applications". AIP Advances. 13 (12). 10.1063/5.0174794.

    DOI: https://doi.org/10.1063/5.0174794
  • [28] H. E. Semary, C. Chesneau, M. A. Aldahlan, I. Elbatal, M. Elgarhy, M. M. Abdelwahab, and E. M. Almetwally. (2024). "Univariate and bivariate extensions of the truncated inverted arctan power distribution with applications". Alexandria Engineering Journal. 100 : 340-356. 10.1016/j.aej.2024.05.044.

    DOI: https://doi.org/10.1016/j.aej.2024.05.044
  • [29] M. Elgarhy, A. Al Mutairi, A. S. Hassan, C. Chesneau, and A. H. Abdel-Hamid. (2023). "Bayesian and non-Bayesian estimations of truncated inverse power Lindley distribution under progressively type-II censored data with applications". AIP Advances. 13 (9). 10.1063/5.0172632.

    DOI: https://doi.org/10.1063/5.0172632
  • [30] M. Elgarhy, N. Alsadat, A. S. Hassan, and C. Chesneau. (2023). "Bayesian inference using MCMC algorithm of sine truncated Lomax distribution with application". AIP Advances. 13 (9). 10.1063/5.0172421.

    DOI: https://doi.org/10.1063/5.0172421
  • [31] N. Alotaibi, I. Elbatal, E. M. Almetwally, S. A. Alyami, A. S. Al-Moisheer, and M. Elgarhy. (2022). "Truncated Cauchy Power Weibull-G Class of Distributions: Bayesian and Non-Bayesian Inference Modelling for COVID-19 and Carbon Fiber Data". Mathematics. 10 (9). 10.3390/math10091565.

    DOI: https://doi.org/10.3390/math10091565
  • [32] D. Soliman, M. A. Hegazy, G. R. Al-Dayian, and A. A. El-Helbawy. (2025). "Statistical Properties and Applications of a New Truncated Zubair- Generalized Family of Distributions". Computational Journal of Mathematical and Statistical Sciences. 4 (1): 222-257. 10.21608/cjmss.2024.322714.1073.

    DOI: https://doi.org/10.21608/cjmss.2024.322714.1073
  • [33] J. J. Swain, S. Venkatraman, and J. R. Wilson. (1988). "Least-squares estimation of distribution functions in johnson's translation system". Journal of Statistical Computation and Simulation. 29 (4): 271-297. 10.1080/00949658808811068.

    DOI: https://doi.org/10.1080/00949658808811068
  • [34] C. K. Onyekwere, O. C. Aguwa, and O. J. Obulezi. (2025). "An Updated Lindley Distribution: Properties, Estimation, Acceptance Sampling, Actuarial Risk Assessment and Applications". Innovation in Statistics and Probability. 1 (1): 1-27. 10.64389/isp.2025.01103.

    DOI: https://doi.org/10.64389/isp.2025.01103
  • [35] Q. N. Husain, A. S. Qaddoori, N. A. Noori, K. N. Abdullah, A. A. Suleiman, and O. S. Balogun. (2025). "New Expansion of Chen Distribution According to the Nitrosophic Logic Using the Gompertz Family". Innovation in Statistics and Probability. 1 (1): 60-75. 10.64389/isp.2025.01105.

    DOI: https://doi.org/10.64389/isp.2025.01105
  • [36] N. A. Noori, M. A. Khaleel, S. A. Khalaf, and S. Dutta. (2025). "Analytical Modeling of Expansion for Odd Lomax Generalized Exponential Distribution in Framework of Neutrosophic Logic: a Theoretical and Applied on Neutrosophic Data". Innovation in Statistics and Probability. 1 (1): 47-59. 10.64389/isp.2025.01104.

    DOI: https://doi.org/10.64389/isp.2025.01104
  • [37] N. A. Noori, K. N. Abdullah, and M. A. Khaleel. (2025). "Development and Applications of a New Hybrid Weibull-Inverse Weibull Distribution". Modern Journal of Statistics. 1 (1): 80-103. 10.64389/mjs.2025.01112.

    DOI: https://doi.org/10.64389/mjs.2025.01112
  • [38] R. Cheng and N. Amin. (1979). "Maximum product of spacings estimation with application to the lognormal distribution". Mathematical Report, Department of Mathematics.  

  • [39] R. C. H. Cheng and N. A. K. Amin. (1983). "Estimating Parameters in Continuous Univariate Distributions with a Shifted Origin". Journal of the Royal Statistical Society Series B: Statistical Methodology. 45 (3): 394-403. 10.1111/j.2517-6161.1983.tb01268.x.

    DOI: https://doi.org/10.1111/j.2517-6161.1983.tb01268.x
  • [40] B. Ranneby. (1984). "The maximum spacing method. An estimation method related to the maximum likelihood method". Scandinavian Journal of Statistics. 11 (2): 93-112.

  • [41] P. D. M. Macdonald. (1971). "Comments and Queries Comment on “An Estimation Procedure for Mixtures of Distributions” by Choi and Bulgren". Journal of the Royal Statistical Society Series B: Statistical Methodology. 33 (2): 326-329. 10.1111/j.2517-6161.1971.tb00884.x.

    DOI: https://doi.org/10.1111/j.2517-6161.1971.tb00884.x
  • [42] L. P. Sapkota, V. Kumar, G. Tekle, H. Alrweili, M. S. Mustafa, and M. Yusuf. (2025). "Fitting Real Data Sets by a New Version of Gompertz Distribution". Modern Journal of Statistics. 1 (1): 25-48. 10.64389/mjs.2025.01109.

    DOI: https://doi.org/10.64389/mjs.2025.01109
  • [43] T. W. Anderson and D. A. Darling. (1952). "Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes". The Annals of Mathematical Statistics. 23 (2): 193-212. 10.1214/aoms/1177729437.

    DOI: https://doi.org/10.1214/aoms/1177729437
  • [44] J. H. K. Kao. (1958). "Computer Methods for Estimating Weibull Parameters in Reliability Studies". IRE Transactions on Reliability and Quality Control. PGRQC-13 : 15-22. 10.1109/ire-pgrqc.1958.5007164.

    DOI: https://doi.org/10.1109/IRE-PGRQC.1958.5007164
  • [45] J. H. K. Kao. (1959). "A Graphical Estimation of Mixed Weibull Parameters in Life-Testing of Electron Tubes". Technometrics. 1 (4): 389-407. 10.1080/00401706.1959.10489870.

    DOI: https://doi.org/10.1080/00401706.1959.10489870
  • [46] T. Kumari, A. Chaturvedi, and A. Pathak. (2018). "Estimation and Testing Procedures for the Reliability Functions of Kumaraswamy-G Distributions and a Characterization Based on Records". Journal of Statistical Theory and Practice. 13 (1).  10.1007/s42519-018-0014-7.

    DOI: https://doi.org/10.1007/s42519-018-0014-7
  • [47] F. Proschan. (1963). "Theoretical Explanation of Observed Decreasing Failure Rate". Technometrics. 5 (3): 375-383. 10.1080/00401706.1963.10490105.

    DOI: https://doi.org/10.1080/00401706.1963.10490105
  • [48] G. Canavos and C. P. Tsokos. (1971). "A Study of an Ordinary and Empirical Bayes Approach of Estimation of Reliability in the Gamma Life Testing Model". Proceedings of IEEE Symposium on Reliability. 1-17. 

  • [49] P. W. Mielke, L. O. Grant, and C. F. Chappell. (1971). "An Independent Replication of the Climax Wintertime Orographic Cloud Seeding Experiment". Journal of Applied Meteorology. 10 (6): 1198-1212. 10.1175/1520-0450(1971)010<1198:Airotc>2.0.Co;2.

  • [50] J. Mazucheli, A. F. Menezes, and S. Dey. (2019). "Unit-Gompertz distribution with applications". Statistica. 79 (1): 25-43.

  • [51] O. M. Khaled, H. M. Barakat, L. A. Al-Essa, and E. M. Almetwally. (2024). "Physics and economic applications by progressive censoring and bootstrapping sampling for extension of power Topp-Leone model". Journal of Radiation Research and Applied Sciences. 17 (2). 10.1016/j.jrras.2024.100898.

    DOI: https://doi.org/10.1016/j.jrras.2024.100898

Paper information