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A Characterization of Joint Distribution of Two-Valued Random Variables and Its Applications

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  • Sharakhmetov, Sh.
  • Ibragimov, R.

Abstract

We obtain an explicit representation for joint distribution of two-valued random variables with given marginals and for a copula corresponding to such random variables. The results are applied to prove a characterization of r-independent two-valued random variables in terms of their mixed first moments. The characterization is used to obtain an exact estimate for the number of almost independent random variables that can be defined on a discrete probability space and necessary conditions for a sequence of r-independent random variables to be stationary.

Suggested Citation

  • Sharakhmetov, Sh. & Ibragimov, R., 2002. "A Characterization of Joint Distribution of Two-Valued Random Variables and Its Applications," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 389-408, November.
    • Handle: RePEc:eee:jmvana:v:83:y:2002:i:2:p:389-408
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    References listed on IDEAS

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    1. Cambanis, Stamatis, 1977. "Some properties and generalizations of multivariate Eyraud-Gumbel-Morgenstern distributions," Journal of Multivariate Analysis, Elsevier, vol. 7(4), pages 551-559, December.
    2. Robertson, James B. & Womack, James M., 1985. "A pairwise independent stationary stochastic process," Statistics & Probability Letters, Elsevier, vol. 3(4), pages 195-199, July.
    3. Parrini, Carl P. & Sklar, Martin J., 1983. "New Thinking about the Marker, 1896–1904: Some American Economists on Investment and the Theory of Surplus Captial," The Journal of Economic History, Cambridge University Press, vol. 43(3), pages 559-578, September.
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    Cited by:

    1. Anat Bracha & Jeremy Gray & Rustam Ibragimov & Boaz Nadler & Dmitry Shapiro & Glena Ames & Donald J. Brown, 2005. "Randomized Sign Test for Dependent Observations on Discrete Choice under Risk," Cowles Foundation Discussion Papers 1526, Cowles Foundation for Research in Economics, Yale University.
    2. Stanislav Anatolyev & Renat Khabibullin & Artem Prokhorov, 2012. "Reconstructing high dimensional dynamic distributions from distributions of lower dimension," Working Papers 12003, Concordia University, Department of Economics.
    3. Fontana, Roberto & Semeraro, Patrizia, 2018. "Representation of multivariate Bernoulli distributions with a given set of specified moments," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 290-303.
    4. Chenguang (Allen) Wu & Achal Bassamboo & Ohad Perry, 2019. "Service System with Dependent Service and Patience Times," Management Science, INFORMS, vol. 65(3), pages 1151-1172, March.
    5. Donald Brown & Rustam Ibragimov & Johan Walden, 2015. "Bounds for path-dependent options," Annals of Finance, Springer, vol. 11(3), pages 433-451, November.
    6. Wei, Li & Yuan, Zhongyi, 2016. "The loss given default of a low-default portfolio with weak contagion," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 113-123.
    7. Donald Brown & Rustam Ibragimov, 2005. "Sign Tests for Dependent Observations and Bounds for Path-Dependent Options," Yale School of Management Working Papers amz2581, Yale School of Management, revised 01 Jul 2005.
    8. Ibragimov, Rustam & Prokhorov, Artem, 2016. "Heavy tails and copulas: Limits of diversification revisited," Economics Letters, Elsevier, vol. 149(C), pages 102-107.
    9. Donald Brown & Rustam Ibragimov, 2005. "Sign Tests for Dependent Observations and Bounds for Path-Dependent Options," Yale School of Management Working Papers amz2581, Yale School of Management, revised 01 Jul 2005.
    10. Donald J. Brown & Rustam Ibragimov, 2005. "Sign Tests for Dependent Observations and Bounds for Path-Dependent Options," Cowles Foundation Discussion Papers 1518, Cowles Foundation for Research in Economics, Yale University.
    11. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2022. "Stochastic representation of FGM copulas using multivariate Bernoulli random variables," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    12. Brown, Donald & Ibragimov, Rustam, 2019. "Sign tests for dependent observations," Econometrics and Statistics, Elsevier, vol. 10(C), pages 1-8.

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