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Copula-based properties of the bivariate Dagum distribution

Abstract

The Dagum distribution plays an important role both in statistical theory and in economics as a model for income distribution. The main goal of this paper was to develop a bivariate extension of the Dagum distribution and study its distributional properties. Also we will study its dependence properties using copula function. Also we derive the cumulative distribution function and probability density function of the maximum and minimum of the bivariate Dagum order statistics. We estimate the parameters of the distribution and demonstrate it on a real data example.

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References

  1. Barreto-Souza W, Lemonte AJ (2013) Bivariate Kumaraswamy distribution: properties and a new method to generate bivariate classes. Statistics 47:1321–1342

    MathSciNet  Article  Google Scholar 

  2. Bartels CPA, van Metelen H (1975) Alternative probability density functions of income. Vrije University Amsterdam: research memorandum no. 29, pp 30

  3. Blomqvist N (1950) On a measure of dependence between two random variables. Ann. Math. Stat. 21:593–600

    MathSciNet  Article  Google Scholar 

  4. Byrd RH, Lu P, Nocedal J, Zhu C (1995) A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput. 16:1190–1208

    MathSciNet  Article  Google Scholar 

  5. Condino F, Giordano S, Popović BV (2015) Reparameterizations of Dagum Distribution, conference: SIS 2015 statistical conference at Treviso, Italy

  6. Dagum C (1977) A new model of personal income-distribution: specification and estimation. Econ Appl 30:413–437

    Google Scholar 

  7. Dagum C (1999) Linking the functional and personal distributions of income. In: Silber J (ed) Handbook on income inequality measurement. Kluwer, London, pp 101–128

    Chapter  Google Scholar 

  8. Domma F (2010) Some properties of the bivariate Burr type III distribution. Statistics 44:203–215

    MathSciNet  Article  Google Scholar 

  9. Gradshteyn IS, Ryzhik IM (2007) Table of integrals, series, and products. In: Jeffrey A, Zwillinger D (eds) 7th edn. Academic Press, New York

  10. Hakamipour N, Mohammadpour A, Nadarajah S (2011) Extremes of a bivariate Pareto distribution. Inf Technol Control 40:83–87

    Google Scholar 

  11. Ker AP (2001) On the maximum of bivariate normal random variables. Extremes 4:185–190

    MathSciNet  Article  Google Scholar 

  12. Kleiber C, Kotz S (2003) Statistical size distributions in economics and actuarial sciences. Wiley, New York

    Book  Google Scholar 

  13. Kundu D, Gupta RD (2009) Bivariate generalized exponential distribution. J Multivar Anal 100:581–593

    MathSciNet  Article  Google Scholar 

  14. Lemmi A, Betti G (2007) Guest Editors’ Introduction. J Econ Inequal 5:259–262

    Article  Google Scholar 

  15. Lien D (2005) On the minimum and maximum of bivariate lognormal random variables. Extremes 8:79–83

    MathSciNet  Article  Google Scholar 

  16. Marshall AW, Olkin I (1967) A multivariate exponential distribution. J Am Stat Assoc 62:30–44

    MathSciNet  Article  Google Scholar 

  17. Meintanis SG (2007) Test of fit for Marshall–Olkin distributions with applications. J Stat Plann Inference 137:3954–3963

    MathSciNet  Article  Google Scholar 

  18. Nelsen RB (1999) An introduction to copulas. In: Lecture Notes in Statistics. Springer, New York

  19. Pareto V (1895) La legge della domanda, Giornale degli Economisti, January 1895, pp 59–68

  20. Pareto V (1896) Ecrits sur la Courbe de la Répartition de la Richesse, Euvres complétes de Vilfredo Pareto publiées sous la direction de Giovanni Busino, Genéve, Librairie Droz, 1965

  21. Pareto V (1897) Cours d’Economie Politique, Lausanne, Rouge, New edition by Bousquet G. H. et G. Busino (1964). Librairie Droz, Genéve

  22. Prudnikov AP, Brychkov YA, Marichev OI (1986) Integrals and series, vol 1. Gordon and Breach, New York

    MATH  Google Scholar 

  23. R Core Team (2014) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. http://www.R-project.org/

  24. Salem ABZ, Mount TD (1974) A convenient descriptive model of income distribution: the gamma density. Econometrica 42:1115–1127

    Article  Google Scholar 

  25. Sarhan AM, Balakrishnan N (2007) A new class of bivariate distributions and its mixture. J Multivar Anal 98:1508–1527

    MathSciNet  Article  Google Scholar 

  26. Wolfram Research, Inc. (2012) Mathematica, Version 9.0, Champaign, IL

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Acknowledgements

We are grateful to the anonymous referees whose comments greatly improved the quality of this manuscript.

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Correspondence to Božidar V. Popović.

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Communicated by Josselin Garnier.

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Popović, B.V., Genç, A.İ. & Domma, F. Copula-based properties of the bivariate Dagum distribution. Comp. Appl. Math. 37, 6230–6251 (2018). https://doi.org/10.1007/s40314-018-0682-7

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Keywords

  • Copula
  • Bivariate Dagum distribution
  • Extreme values
  • Dependency

Mathematics Subject Classification

  • 60G70
  • 62G32
  • 62E15
  • 62H20