The New Dagum-X Family of Distributions: Properties and Applications

Main Article Content

Amani S. Alghamdi, Huda Alghamdi, Aisha Fayomi


Various statistical distributions are still being used extensively over the previous decades for modeling data in numerous areas such as engineering, sciences, and finance. Nonetheless, in a lot of applied areas, there is a continuous need for expanded forms of these distributions. However, many common distributions do not fit the data well. Thus, new distributions have been constructed in literature. The purpose of this article is to present a new family of distributions using the Dagum distribution as a generator and to study its properties such as hazard rate functions, moments, quantile function, ordered statistics and Renyi entropy. Moreover, one sub model called Dagum-Frechet distribution is discussed with some of its properties. The maximum likelihood estimation is employed to estimate the parameters of the proposed distribution, and the confidence intervals are obtained. Finally, two real data sets are analyzed to illustrate the performance of the purposed distribution.

Article Details


  1. N. Eugene, C. Lee, F. Famoye, Beta-Normal Distribution and Its Applications, Commun. Stat. - Theory Methods. 31 (2002), 497-512.
  2. G.M. Cordeiro, M. de Castro, A New Family of Generalized Distributions, J. Stat. Comput. Simul. 81 (2011), 883-898.
  3. G.M. Cordeiro, E.M. Ortega, D.C. da Cunha, The Exponentiated Generalized Class of Distributions, J. Data Sci. 11 (2013), 1-27.
  4. A. Alzaatreh, F. Famoye, C. Lee, The Gamma-Normal Distribution: Properties and Applications, Comput. Stat. Data Anal. 69 (2014), 67-80.
  5. M.H. Tahir, G.M. Cordeiro, A. Alzaatreh, M. Mansoor, M. Zubair, The Logistic-X Family of Distributions and Its Applications, Commun. Stat. - Theory Methods. 45 (2016), 7326-7349.
  6. G.M. Cordeiro, A.Z. Afify, E.M.M. Ortega, A.K. Suzuki, M.E. Mead, The Odd Lomax Generator of Distributions: Properties, Estimation and Applications, J. Comput. Appl. Math. 347 (2019), 222-237.
  7. M. Mahmoud, R. Mandouh, R. Abdelatty, Lomax-Gumbel {Frechet}: A New Distribution, J. Adv. Math. Computer Sci. 31 (2019), 1-19.
  8. Z. Ahmad, The Zubair-G Family of Distributions: Properties and Applications, Ann. Data. Sci. 7 (2018), 195-208.
  9. A. Fayomi, S. Khan, M.H. Tahir, A. Algarni, F. Jamal, R. Abu-Shanab, A New Extended Gumbel Distribution: Properties and Application, PLoS ONE. 17 (2022), e0267142.
  10. A. Alzaatreh, C. Lee, F. Famoye, A New Method for Generating Families of Continuous Distributions, Metron. 71 (2013), 63-79.
  11. M. Zenga, La Curtosi, Statistica. 56 (1996), 87-102.
  12. M. Polisicchio, M. Zenga, Kurtosis Diagram for Continuous Random Variables, Metron. 55 (1997), 21-41.
  13. F. Domma, Kurtosis Diagram for the Log-Dagum Distribution, Stat. Appl. 2 (2004), 3–23.
  14. F. Domma, P.F. Perri, Some Developments on the Log-Dagum Distribution, Stat. Methods Appl. 18 (2008), 205-220.
  15. B.O. Oluyede, S. Rajasooriya, The Mc-Dagum Distribution and Its Statistical Properties with Applications, Asian J. Math. Appl. 1 (2013), ama085.
  16. B.O. Oluyede, Y. Ye, Weighted Dagum and Related Distributions, Afr. Mat. 25 (2013), 1125-1141.
  17. A. de O. Silva, L.C.M. da Silva, G.M. Cordeiro, The Extended Dagum Distribution: Properties and Application, J. Data Sci. 13 (2021), 53-72.
  18. B.O. Oluyede, G. Motsewabagale, S. Huang, G. Warahena-Liyanage, M. Pararai, The Dagum-Poisson Distribution: Model, Properties Application, Electron. J. Appl. Stat. Anal. 9 (2016), 169-197.
  19. S. Nasiru, P.N. Mwita, O. Ngesa, Exponentiated Generalized Exponential Dagum Distribution, J. King Saud Univ. - Sci. 31 (2019), 362-371.
  20. H.S. Bakouch, M.N. Khan, T. Hussain, C. Chesneau, A Power Log-Dagum Distribution: Estimation and Applications, J. Appl. Stat. 46 (2018), 874-892.
  21. A.Z. Afify, M. Alizadeh, The Odd Dagum Family of Distributions: Properties and Applications, J. Appl. Probab. Stat. 15 (2020), 45–72.
  22. L. Rayleigh, XII. On the Resultant of a Large Number of Vibrations of the Same Pitch and of Arbitrary Phase, London Edinburgh Dublin Phil. Mag. J. Sci. 10 (1880), 73-78.
  23. A. Alzaghal, F. Famoye, C. Lee, Exponentiated T-X Family of Distributions with Some Applications, Int. J. Stat. Probab. 2 (2013), 31-49.
  24. A.S. Hassan, M. Elgarhy, Z. Ahmad, Type II Generalized Topp-Leone Family of Distributions: Properties and Applications, J. Data Sci. 17 (2019), 638-658.
  25. S. Nadarajah and S. Kotz, The Exponentiated Frechet Distribution, Interstat Electron. J. 14 (2003), 1-7.
  26. T. Sultana, M. Aslam, J. Shabbir, Bayesian Analysis of the Mixture of Frechet Distribution under Different Loss Functions, Pak. J. Stat. Oper. Res. 13 (2017), 501-528.
  27. P.E. Oguntunde, M.A. Khaleel, M.T. Ahmed, H.I. Okagbue, The Gompertz Frechet distribution: Properties and applications, Cogent Math. Stat. 6 (2019), 1568662.
  28. M. Hamed, F. Aldossary, A.Z. Afify, The Four-Parameter Frechet Distribution: Properties and Applications, Pak. J. Stat. Oper. Res. 16 (2020), 249–264.
  29. S. Nadarajah, A.K. Gupta, The Beta Frechet Distribution, Far East J. Theor. Stat. 14 (2004), 15-24.
  30. R.V. da Silva, T.A.N. de Andrade, D.B.M. Maciel, R.P.S. Campos, G.M. Cordeiro, A New Lifetime Model: The Gamma Extended Frechet Distribution, J. Stat. Theory Appl. 12 (2013), 39-54.
  31. M. Mansoor, M.H. Tahir, A. Alzaatreh, G.M. Cordeiro, M. Zubair, S.A. Ghazali, An Extended Frechet Distribution: Properties and Applications, J. Data Sci. 14 (2021), 167-188.
  32. M. Frechet, Sur les Ensembles Compacts de Fonctions Mesurables, Fundam. Math. 9 (1927), 25–32.
  33. P.L. Ramos, F. Louzada, E. Ramos, S. Dey, The Frechet distribution: Estimation and application - An overview, J. Stat. Manage. Syst. 23 (2019), 549-578.
  34. G.M. Cordeiro, R.B. da Silva, The Complementary Extended Weibull Power Series Class of Distributions, Ciência e Natura, 36 (2014), 1-13.
  35. L. Tomy, J. Gillariose, A Generalized Rayleigh Distribution and Its Application, Biometrics Biostat. Int. J. 8 (2019), 139-143.