IDEAS home Printed from https://ideas.repec.org/a/spr/metron/v75y2017i1d10.1007_s40300-016-0104-9.html
   My bibliography  Save this article

Trivariate Burr-III copula with applications to income data

Author

Listed:
  • Lucio De Capitani

    (Università degli Studi di Milano-Bicocca)

  • Federica Nicolussi

    (Università Cattolica del Sacro Cuore)

  • Alessandro Zini

    (Università degli Studi di Milano-Bicocca)

Abstract

In this work, Bivariate Burr-III copula is extended to the trivariate case. This copula seems to be very general and analytically manageable and it provides an alternative to the commonly employed elliptical copulas (such as the Gaussian or the Stutent’s t ones) since they have, roughly, the same number of parameters. Several applications to income and wine data are described in the paper. They show that the Trivariate Burr-III copula is, in general, able to capture the dependence structure implicit in observed trivariate data. Moreover, they show that the third-order interaction parameter results, in some cases, significant at $$1\%$$ 1 % significance level while, in other cases, it can be removed from the fitted model. The ability of the Trivariate Burr-III copula in representing the dependence structure implicit in the considered data is compared with the ones of other well known copulas: the Clayton copula, the t copula, and the Skew-t copula. It results that the Trivariate Burr-III copula provides a good fitting and turns out to be the best performer in fitting the considered wine data but, on income data, the best performers are the t and Skew-t copulas. The over-performance of the last two copulas on income data is probably due to their ability in representing right-tail dependence (a kind of dependence that is not taken into account by the Trivariate Burr-III copula).

Suggested Citation

  • Lucio De Capitani & Federica Nicolussi & Alessandro Zini, 2017. "Trivariate Burr-III copula with applications to income data," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 109-124, April.
    • Handle: RePEc:spr:metron:v:75:y:2017:i:1:d:10.1007_s40300-016-0104-9
    DOI: 10.1007/s40300-016-0104-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40300-016-0104-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s40300-016-0104-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Christian Kleiber, 2008. "A Guide to the Dagum Distributions," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 6, pages 97-117, Springer.
    2. Alberto Arcagni & Francesco Porro, 2013. "On the parameters of Zenga distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(3), pages 285-303, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vladimir Hlasny, 2021. "Parametric representation of the top of income distributions: Options, historical evidence, and model selection," Journal of Economic Surveys, Wiley Blackwell, vol. 35(4), pages 1217-1256, September.
    2. Camelia Minoiu & Sanjay Reddy, 2014. "Kernel density estimation on grouped data: the case of poverty assessment," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 12(2), pages 163-189, June.
    3. Markus P. A. Schneider, 2013. "Race & Gender Differences in the Experience of Earnings Inequality in the US from 1995 to 2010," Working Papers 1303, New School for Social Research, Department of Economics.
    4. Faustino Prieto & Jos'e Mar'ia Sarabia & Enrique Calder'in-Ojeda, 2020. "The risk of death in newborn businesses during the first years in market," Papers 2011.11776, arXiv.org.
    5. A. Abigail Payne & Justin Smith, 2015. "Does income inequality increase charitable giving?," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 48(2), pages 793-818, May.
    6. Tsvetana Spasova, 2019. "Regional Income Distribution in the European Union: A Parametric Approach," Research on Economic Inequality, in: What Drives Inequality?, volume 27, pages 1-18, Emerald Group Publishing Limited.
    7. Markus Schneider, 2013. "Illustrating the Implications of How Inequality is Measured: Decomposing Earnings Inequality by Race and Gender," Journal of Labor Research, Springer, vol. 34(4), pages 476-514, December.
    8. Melanie Krause, 2014. "Parametric Lorenz Curves and the Modality of the Income Density Function," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 60(4), pages 905-929, December.
    9. Ivana Malá, 2013. "Použití konečných směsí logaritmicko-normálních rozdělení pro modelování příjmů českých domácností [The Use of Finite Mixtures of Lognormal Distribution for the Modelling of Household Income Distri," Politická ekonomie, Prague University of Economics and Business, vol. 2013(3), pages 356-372.
    10. Kazuhiko Kakamu, 2016. "Simulation Studies Comparing Dagum and Singh–Maddala Income Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 48(4), pages 593-605, December.
    11. Francesca Greselin & Alina Jȩdrzejczak, 2020. "Analyzing the Gender Gap in Poland and Italy, and by Regions," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 26(4), pages 433-447, November.
    12. Alberto Arcagni & Francesco Porro, 2013. "On the parameters of Zenga distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(3), pages 285-303, August.
    13. Brzezinski, Michal, 2014. "Empirical modeling of the impact factor distribution," Journal of Informetrics, Elsevier, vol. 8(2), pages 362-368.
    14. Herrera, Roberto & Pino, Gabriel, 2023. "The effect of administrative divisions on the distribution of individual income in the new territories of Chile," World Development, Elsevier, vol. 171(C).
    15. Smith, V. Kerry, 2023. "Student debt forgiveness, residential energy credits, and equity," Economics Letters, Elsevier, vol. 222(C).
    16. Corrado Benassi & Alessandra Chirco & Caterina Colombo, 2019. "Vertical differentiation beyond the uniform distribution," Journal of Economics, Springer, vol. 126(3), pages 221-248, April.
    17. Refah Alotaibi & Hoda Rezk & Sanku Dey & Hassan Okasha, 2021. "Bayesian estimation for Dagum distribution based on progressive type I interval censoring," PLOS ONE, Public Library of Science, vol. 16(6), pages 1-17, June.
    18. Walter, Paul & Weimer, Katja, 2018. "Estimating poverty and inequality indicators using interval censored income data from the German microcensus," Discussion Papers 2018/10, Free University Berlin, School of Business & Economics.
    19. Francesca Greselin & Ričardas Zitikis, 2018. "From the Classical Gini Index of Income Inequality to a New Zenga-Type Relative Measure of Risk: A Modeller’s Perspective," Econometrics, MDPI, vol. 6(1), pages 1-20, January.
    20. Małgorzata Ćwiek & Kamila Trzcińska, 2023. "Assessment of goodness of fit of income distribution in France and Germany based on the Zenga distribution," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(5), pages 4013-4027, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metron:v:75:y:2017:i:1:d:10.1007_s40300-016-0104-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.