IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v101y2010i8p1859-1871.html
   My bibliography  Save this article

A class of models for uncorrelated random variables

Author

Listed:
  • Ebrahimi, Nader
  • Hamedani, G.G.
  • Soofi, Ehsan S.
  • Volkmer, Hans

Abstract

We consider the class of multivariate distributions that gives the distribution of the sum of uncorrelated random variables by the product of their marginal distributions. This class is defined by a representation of the assumption of sub-independence, formulated previously in terms of the characteristic function and convolution, as a weaker assumption than independence for derivation of the distribution of the sum of random variables. The new representation is in terms of stochastic equivalence and the class of distributions is referred to as the summable uncorrelated marginals (SUM) distributions. The SUM distributions can be used as models for the joint distribution of uncorrelated random variables, irrespective of the strength of dependence between them. We provide a method for the construction of bivariate SUM distributions through linking any pair of identical symmetric probability density functions. We also give a formula for measuring the strength of dependence of the SUM models. A final result shows that under the condition of positive or negative orthant dependence, the SUM property implies independence.

Suggested Citation

  • Ebrahimi, Nader & Hamedani, G.G. & Soofi, Ehsan S. & Volkmer, Hans, 2010. "A class of models for uncorrelated random variables," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1859-1871, September.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:8:p:1859-1871
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(10)00070-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. de Paula, Aureo, 2008. "Conditional Moments and Independence," The American Statistician, American Statistical Association, vol. 62, pages 219-221, August.
    2. Hamedani, G. G. & S. Key, Eric & Volkmer, Hans, 2004. "Solution to a functional equation and its application to stable and stable-type distributions," Statistics & Probability Letters, Elsevier, vol. 69(1), pages 1-9, August.
    3. Hamedani, G. G. & Volkmer, H. W., 2009. "Letter to the Editor," The American Statistician, American Statistical Association, vol. 63(3), pages 295-295.
    4. Shaw, W.T. & Lee, K.T.A., 2008. "Bivariate Student t distributions with variable marginal degrees of freedom and independence," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1276-1287, July.
    5. Rodríguez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2004. "A new class of bivariate copulas," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 315-325, February.
    6. Jones, M. C., 2002. "A dependent bivariate t distribution with marginals on different degrees of freedom," Statistics & Probability Letters, Elsevier, vol. 56(2), pages 163-170, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Schennach, Susanne M., 2019. "Convolution without independence," Journal of Econometrics, Elsevier, vol. 211(1), pages 308-318.
    2. Ebrahimi, Nader & Jalali, Nima Y. & Soofi, Ehsan S., 2014. "Comparison, utility, and partition of dependence under absolutely continuous and singular distributions," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 32-50.
    3. Vexler, Albert & Zou, Li, 2022. "Linear projections of joint symmetry and independence applied to exact testing treatment effects based on multidimensional outcomes," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    4. Chen, Xiaohong & Linton, Oliver & Yi, Yanping, 2017. "Semiparametric identification of the bid–ask spread in extended Roll models," Journal of Econometrics, Elsevier, vol. 200(2), pages 312-325.
    5. Alessandra Carleo & Carlo Domenico Mottura & Luca Passalacqua, 2011. "The mathematical framework underlying the "scenarios" approach for derivate transactions by italian local authorities," Departmental Working Papers of Economics - University 'Roma Tre' 0127, Department of Economics - University Roma Tre.

    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. S.T. Boris Choy & Cathy W.S. Chen & Edward M.H. Lin, 2014. "Bivariate asymmetric GARCH models with heavy tails and dynamic conditional correlations," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1297-1313, July.
    2. Mukhtar M. Salah & M. El-Morshedy & M. S. Eliwa & Haitham M. Yousof, 2020. "Expanded Fréchet Model: Mathematical Properties, Copula, Different Estimation Methods, Applications and Validation Testing," Mathematics, MDPI, vol. 8(11), pages 1-29, November.
    3. Mahmoud M. Mansour & Mohamed Ibrahim & Khaoula Aidi & Nadeem Shafique Butt & Mir Masoom Ali & Haitham M. Yousof & Mohamed S. Hamed, 2020. "A New Log-Logistic Lifetime Model with Mathematical Properties, Copula, Modified Goodness-of-Fit Test for Validation and Real Data Modeling," Mathematics, MDPI, vol. 8(9), pages 1-20, September.
    4. Mukhopadhyay, Nitis, 2009. "On px1 dependent random variables having each (p-1)x1 sub-vector made up of IID observations with examples," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1585-1589, July.
    5. Paolella, Marc S. & Polak, Paweł, 2015. "ALRIGHT: Asymmetric LaRge-scale (I)GARCH with Hetero-Tails," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 282-297.
    6. Cécile Amblard & Stéphane Girard, 2009. "A new extension of bivariate FGM copulas," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(1), pages 1-17, June.
    7. Tomav{z} Kov{s}ir & Matjav{z} Omladiv{c}, 2018. "Reflected maxmin copulas and modelling quadrant subindependence," Papers 1808.07646, arXiv.org, revised Dec 2018.
    8. Baker, Rose, 2008. "An order-statistics-based method for constructing multivariate distributions with fixed marginals," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2312-2327, November.
    9. Arbel, Julyan & Crispino, Marta & Girard, Stéphane, 2019. "Dependence properties and Bayesian inference for asymmetric multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    10. Saminger-Platz Susanne & Kolesárová Anna & Šeliga Adam & Mesiar Radko & Klement Erich Peter, 2021. "New results on perturbation-based copulas," Dependence Modeling, De Gruyter, vol. 9(1), pages 347-373, January.
    11. Jia-Han Shih & Takeshi Emura, 2019. "Bivariate dependence measures and bivariate competing risks models under the generalized FGM copula," Statistical Papers, Springer, vol. 60(4), pages 1101-1118, August.
    12. Indranil Ghosh, 2017. "Bivariate Kumaraswamy Models via Modified FGM Copulas: Properties and Applications," JRFM, MDPI, vol. 10(4), pages 1-13, November.
    13. Christine Amsler & Artem Prokhorov & Peter Schmidt, 2021. "A new family of copulas, with application to estimation of a production frontier system," Journal of Productivity Analysis, Springer, vol. 55(1), pages 1-14, February.
    14. Jorge Navarro & Franco Pellerey & Miguel A. Sordo, 2020. "Weak Dependence Notions and Their Mutual Relationships," Mathematics, MDPI, vol. 9(1), pages 1-27, December.
    15. Jiang, Jun & Tang, Qihe, 2011. "The product of two dependent random variables with regularly varying or rapidly varying tails," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 957-961, August.
    16. Matthew Masten & Alexandre Poirier, 2016. "Partial independence in nonseparable models," CeMMAP working papers CWP26/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    17. repec:bpj:demode:v:6:y:2018:i:1:p:156-177:n:10 is not listed on IDEAS
    18. Kahkashan Afrin & Ashif S Iquebal & Mostafa Karimi & Allyson Souris & Se Yoon Lee & Bani K Mallick, 2020. "Directionally dependent multi-view clustering using copula model," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-18, October.
    19. Longobardi, Maria & Pellerey, Franco, 2019. "On the role of dependence in residual lifetimes," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 56-64.
    20. Mao, Tiantian & Yang, Fan, 2015. "Risk concentration based on Expectiles for extreme risks under FGM copula," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 429-439.
    21. Schmid, Friedrich & Schmidt, Rafael, 2007. "Multivariate extensions of Spearman's rho and related statistics," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 407-416, February.

    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:eee:jmvana:v:101:y:2010:i:8:p:1859-1871. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.