A new log dagum singh maddala TX family of distribution

  • Authors

    • Aneeqa Khadim Mirpur university of Science and technology
    • Aamir Saghir Department of Mathematics Mirpur University of Science and Technology (MUST)‎‎ Mirpur-10250 AJK, Pakistan‎
    • Tassadaq Hussain Department of Mathematics Mirpur University of Science and Technology (MUST)‎‎ Mirpur-10250 AJK, Pakistan‎
    • M. Shakil‎ Department of Mathematics Miami Dade College Hialeah FL33024, USA‎

    Received date: January 2, 2025

    Accepted date: January 27, 2025

    Published date: February 20, 2025

    https://doi.org/10.14419/gxf6wa90
  • Log-Dagum Distribution; Probability Distributions; Characterization; Simulation Study; ‎Maximum Likelihood; Parameter Estimation; Singh Maddala Distribution.

  • Abstract

    This study introduces the Log-Dagum Singh Maddala (4P) distribution, a significant ‎contribution to the field of continuous distributions. We investigate its statistical properties ‎including probability density, hazard rate, survival functions, quantiles, and order statistics. ‎The distribution is thoroughly characterized using multiple approaches and maximum ‎likelihood estimation is used to determine the parameters. The model's effectiveness is ‎evaluated using three real-world datasets and a comparative analysis with established ‎distributions highlights its advantages. The results confirm the excellence of the proposed ‎model demonstrating its practical significance in real data analysis‎.

  • References

    1. Afify A. Z., M. Alizadeh. “The Odd Dagum Family of Distributions: Properties and‎ Applications”, journal of Applied Probability and Statistics, Vol. 15, 2020, 45–72.‎
    2. Ahsanullah M., Nevzorov V. B., and Shakil M. “An Introduction to Order Statistics”, ‎Atlantis Press, Paris, France, 2013a, 1879-6893.‎ https://doi.org/10.2991/978-94-91216-83-1.
    3. Ahsanullah M. “Record Statistics”, Nova Science Publishers, New York, USA, 1995.‎
    4. Alzaatreh A., Lee C., and Famoye F. “A new method for generating families of‎ continuous distributions”, Metron, Vol. 71, No. 1, 2013, 63-79. ‎ https://doi.org/10.1007/s40300-013-0007-y.
    5. Alzaatreh A., Famoye F. and Lee C. “T-normal family of distributions: A new‎ approach to generalize the normal distribution”, Journal of Statistical Distributions ‎‎ and Applications, Vol. 16, No.1. 2014b. ‎ https://doi.org/10.1186/2195-5832-1-16.
    6. Alzaghal A., Famoye F., and Lee C. “Exponentiated T-X family of distributions‎ with some applications”, International Journal of Prob-ability and Statistics, Vol. ‎‎2, No. 3, ‎‎ 2013, 31–49. ‎ https://doi.org/10.5539/ijsp.v2n3p31.
    7. Aljarrah M. A., Lee C., and Famoye F. “On generating T-X family of distributions‎ using quantile functions”, Journal of Statistical Dis-tributions and Applications, Vol. ‎‎2,‎‎ No.1.2014.‎ https://doi.org/10.1186/2195-5832-1-2.
    8. Arnold B. C., Balakrishnan Nagaraja H. N. “First Course in Order Statistics”, ‎Wiley, New York, USA, 2005.‎
    9. Aslam M., Asghar Z., Hussain Z., and Farooq S. S. “A modified T-X family of‎ distributions classical and Bayesian analysis”, Journal of Taibah University for ‎Science, Vol. 14, No. 1, 2020, 254–264.‎ https://doi.org/10.1080/16583655.2020.1732642.
    10. Cordeiro G.M., Ortega E.M.M.and da Cunha D.C.C. “The exponentiated ‎generalized class of distributions”, Journal of Data Science, Vol. 11, 2013.1–27.‎ https://doi.org/10.6339/JDS.201301_11(1).0001.
    11. Cordeiro G.M., de Castro, M. “A new family of generalized distributions”, Journal ‎of‎ Statistical Computation and Simulation, 81, 7, 2011. 883–898‎ https://doi.org/10.1080/00949650903530745.
    12. David H. A., Nagaraja H. N. Order Statistics, Third Edition, Wiley, New York, ‎‎ USA, 2003.‎ https://doi.org/10.1002/0471722162.
    13. Domma F. “Kurtosis diagram for the log-Dagum distribution”, Statistica and‎ Applicatzioni, Vol. 2, 2004, 3–23.‎
    14. Eugene N., Lee C., and Famoye F. “Beta-normal distribution and its ‎applications”,‎‎ Communication Statistical Theory & Methods, Vol.31, No.4, 2002. 497 – 512.‎ https://doi.org/10.1081/STA-120003130.
    15. Handique L., Akbar M., Mohsin M., and Jamal F. Properties and applications ‎of a new member of the T-X family of distributions, Thailand statistician, ‎Vol.19, 2021, 248-260.‎
    16. Jamal F., Nasir M. A. (2019). “Some new members of the T-X family of ‎distributions”, ‎‎ Proceedings of the 17th International Confer-ence on Statistical Sciences, ‎Lahore,‎‎ Pakistan.2019.‎
    17. Khadim A., Saghir A., Hussain T., Shakil M., and Ahsanullah M. “Log Dagum‎‎ Weibull distribution”, Applied and Computational Mathematics, Vol.10, No.5, ‎‎2021,‎‎ 100-113.‎ https://doi.org/10.11648/j.acm.20211005.11.
    18. Nevzorov V. B. “Records: Mathematical Theory-Translation of Mathematical‎ Monograph”, American Mathematical Society, Rhode Is-land, USA. 2001.‎ https://doi.org/10.1090/mmono/194.
    19. Polisicchio M., and Zenga M. “Kurtosis diagram for continuous variables”, ‎Metron, ‎‎ Vol.55, 1997, 21–41.‎
    20. Rasha M. Mandouh., Mahmoud R., and Rasha E. Abdelatty. “A new ‎‎(T X^θ) family‎ of distributions”, Scientific Reports, vol.14, 2024.‎ https://doi.org/10.1038/s41598-023-49425-2.
    21. Risti´c M. M., and Balakrishnan N. “The gamma-exponentiated exponential‎ Distribution”, Journal of Statistical Computation and Simu-lation, Vol. 82, 2012, ‎‎ 1191–1206.‎ https://doi.org/10.1080/00949655.2011.574633.
    22. Shakil M., Kibria B.M., and Ahsanullah M. “Some Inferences on Dagum (4P)‎‎ Distribution”, Statistical Distribution and their Applica-tions, Vol.154, 2021, 1-33.‎
    23. ‎Shakil M., Kibria B. M., Singh J.N., and Ahsanullah M. “On Burr (4P) ‎Distribution‎ Application of Breaking Stress Data” , Statistical Distributions and their ‎Applications, ‎‎ Vol. 2, 2021, 190-199. ‎ https://doi.org/10.1080/00949655.2011.574633.
    24. Singh S.K., and Mandela G.S. “A function for size distribution of Incomes”,‎‎ Econometric, Vol. 44, 1976, 963–970. ‎ https://doi.org/10.2307/1911538.
    25. Tahir M.H., Zubair M., Mansoor M., Gauss M., Cordeiro Morad ‎Alizadeh., and ‎‎ Hamedani G. G. “A new Weibull-G family of distribu-tions”, Hacettepe Journal‎ of Mathematics and Statistics, Vol. 45, No. 2, 2016, 629-647.‎ https://doi.org/10.15672/HJMS.2015579686.

  • Downloads

  • Received date: January 2, 2025

    Accepted date: January 27, 2025

    Published date: February 20, 2025