International E-publication: Publish Projects, Dissertation, Theses, Books, Souvenir, Conference Proceeding with ISBN.  International E-Bulletin: Information/News regarding: Academics and Research

Topp-Leone Dagum Distribution: Properties and its Applications

Author Affiliations

  • 1Department of Statistics, Punjab College Hasilpur, Pakistan

Res. J. Mathematical & Statistical Sci., Volume 8, Issue (1), Pages 16-30, January,12 (2020)

Abstract

In this work, we acquaint four parametric Topp-Leone Dagum distribution using the Topp-Leone-I (Type-I Topp-Leone) G class of distribution. We obtain some basic statistical properties, incomplete rth moments, mean deviation from mean, reliability and income inequality measures of the distribution, from graphical point of view we provide plots both its density and decreasing hazard function with assumed parametric values. We find Renyi and Tsallis entropies as well. We examine both parameter estimation methods, probability weighted moments and maximum likelihood. In the end we suggest four applications where this distribution is considered as best fitted model to the sub models of Dagum distribution and other related models in which Burr, Log-Dagum, generalized Dagum and Lomax distributions are include.

References

  1. Dagum C. (1977)., A new model of personal income distribution: specification and estimation., Economie Appliqu´ee, 30, 413-437.
  2. Burr I.W. (1942)., Cumulative frequency functions., Annals of Mathematical Statistics, 13, 215-232.
  3. Domma F. (2004)., Kurtosis diagram for the log-Dagum distribution., Statistica and Applicatzioni, 2, 3-23.
  4. Kleiber C. and Kotz S. (2003)., Statistical Size Distributions in Economics and Actuarial Sciences., New York: Wiley, ISBN: 978-0-471-15064-0.
  5. Kleiber C. (2008)., A guide to the Dagum distributions., In: Duangkamon, C. (Eds.), Modeling Income Distributions and Lorenz Curves Series, Springer, New York, 97-117.
  6. Shehzad M.N. and Asghar Z. (2013)., Comparing TL-moments, L–moments and conventional moments of Dagum distribution by simulated data., Colombian Journal of Statistics, 36, 79-93.
  7. Khan M.Z. (2013)., Dagum, Inverse Dagum and Generalized Dagum Income Size Distributions., Unpublished M.Phil. Thesis, Department of Statistics, The Islamia University of Bahawalpur, Pakistan.
  8. Dey S., Al-Zahrani B. and Basloom S. (2017)., Dagum distribution: properties and different methods of estimation., International Journal of Statistics and Probability, 6(2), 74-92.
  9. Domma F., Latorre G. and Zenga M. (2012)., The dagum distribution in reliability analysis., Statistica & Applicazioni, 10(2), 97-113.
  10. Oluyede B.O. and Ye Y. (2014)., Weighted Dagum and related distributions., Afrika Matematika, 25(4), 1125-1141. https://doi.org/10.1007/s13370-013-0176-0
  11. Domma F. and Condino F. (2013)., The beta-Dagum distribution: Definition and properties., Communications in Statistics–Theory and Methods, 42(22), 4070-4090.
  12. Eugene N., Lee C. and Famoye F. (2002)., Beta-normal distribution and its applications., Communications in Statistics–Theory and Methods, 31, 497-512.
  13. Jones M.C. (2004)., Families of distributions arising from the distributions of order statistics., Test 13, 1-43.
  14. Oluyede B.O. and Rajasooriya S. (2013)., The Mc-Dagum distribution and its statistical properties with applications., Asian Journal of Mathematics and Applications Article ID ama 0085, 16 pages.
  15. Huang S. and Oluyede B.O. (2014)., Exponentiated Kumaraswamy-Dagum distribution with applications to income and lifetime data., Journal of Statistical Distributions and Applications, 1(8), 1-20.
  16. Tahir M.H., Cordeiro G.M., Mansoor M., Zubair M. and Alizadeh M. (2016)., The Weibull–Dagum distribution: Properties and applications., Communications in Statistics - Theory and Methods, 45(24), 7376-7398.
  17. Bourguignon M., Silva R.B. and Cordeiro G.M. (2014)., The Weibull–G family of probability distributions., Journal of Data Science, 12, 53-68.
  18. Silva A.O., da Silva L.C.M. and Cordeiro G.M. (2015)., The extended Dagum distribution: properties and applications., Journal of Data Science, 13, 53-72.
  19. Nasiru S., Mwita P.N. and Negesa O. (2017)., Exponentiated generalized exponential Dagum distribution., Journal of King Saud University –Science, 31, 362-371.
  20. Al-Shomrani A., Arif O., Shawky A., Hanif S. and Shahbaz M.Q. (2016)., Topp-Leone family of distributions: some properties and application., Pakistan Journal of Statistics and Operation Research, 12(3), 443-451.
  21. Kenney J. and Keeping E. (1962)., Mathematics of Statistics., Volume 1. Princeton
  22. Moors J.J.A. (1988)., A quantile alternative for kurtosis., Journal of the Royal Statistical Society: Series D (The Statistician), 37(1), 25-32.
  23. Gini C. (1914)., Sulla misura della concentrazione e della variabilita del caratteri., Atti del R. Instituto Veneto, 73, 1913-1914.
  24. Lorenz M.O. (1905)., Methods of measuring the concentration of wealth., Publications of the American statistical association, 9(70), 209-219.
  25. Bonferroni C. (1930)., Elmenti di statistica generale., Libreria Seber, Firenze.
  26. Cowell F.A. (1980)., On the structure of additive inequality measures., The Review of Economic Studies, 47(3), 521-531.
  27. Pietra G. (1915)., Delle relazioni fra indici di variabilit´a, note I e II., Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti, 74, 775-804.
  28. Zenga M. (1996)., La curtosi (Kurtosis)., Statistica 56, 87-101.
  29. Rényi A. (1961)., On measures of entropy and information., University of California Press, Berkeley, California, 547-561.
  30. Havrda J. and Charvat F. (1967)., Quantification method in classification processes: concept of structural alpha-entropy., Kybernetika, 3, 30-35.
  31. Tsallis C. (1988)., Possible generalization of Boltzmann-Gibbs statistics., Journal of Statistical Physics, 52, 479-487.
  32. Greenwood J.A., Landwehr J.M., Matalas N.C. and Wallis J.R. (1979)., Probability weighted moments: definition and relation to parameters of several distribution expressible in inverse form., Water Resources Research, 15(5), 1049-1054.
  33. Proschan F. (1963)., Theoretical explanation of observed decreasing failure rate., Technometrics, 5(3), 375-383.
  34. Harter H.L. and Moore A.H. (1965)., Maximum-likelihood estimation of the parameters of gamma and Weibull populations from complete and from censored samples., Technometrics, 7(4), 639-643.
  35. Bhatti F.A., Ali A., Hamedani G.G. and Ahmad M. (2018)., On Generalized Log Burr XII distribution., Pakistan Journal of Statistics and Operation Research, 14(3), 615-643.
  36. Murthy D.N.P., Xie M. and Jiang R. (2004)., Weibull models, Series in Probability and Statistics., John Wiley, New Jersey.
  37. Bhaumik D.K., Kapur K.G. and Gibbons R.D. (2009)., Testing parameters of a gamma distribution for small samples., Technometrics, 51(3), 326-334.