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Copula function for fuzzy random variables: applications in measuring association between two fuzzy random variables

Author

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  • Vahid Ranjbar

    (Golestan University)

  • Gholamreza Hesamian

    (Payame Noor University)

Abstract

In this paper, a notion of fuzzy copula function is introduced by defining joint distribution function of two fuzzy random variables. Using some lemmas, it is proven that the extended fuzzy copula satisfies many desired properties used for non-fuzzy data. The proposed fuzzy copula is then applied to construct some common non-parametric measures of association between two fuzzy random variables. The proposed methods is then illustrated via some numerical examples.

Suggested Citation

  • Vahid Ranjbar & Gholamreza Hesamian, 2020. "Copula function for fuzzy random variables: applications in measuring association between two fuzzy random variables," Statistical Papers, Springer, vol. 61(1), pages 503-522, February.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:1:d:10.1007_s00362-017-0944-2
    DOI: 10.1007/s00362-017-0944-2
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    References listed on IDEAS

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    1. Shapiro, Arnold F., 2009. "Fuzzy random variables," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 307-314, April.
    2. Low, Rand Kwong Yew & Alcock, Jamie & Faff, Robert & Brailsford, Timothy, 2013. "Canonical vine copulas in the context of modern portfolio management: Are they worth it?," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3085-3099.
    3. Gholamreza Hesamian & Jalal Chachi, 2015. "Two-sample Kolmogorov–Smirnov fuzzy test for fuzzy random variables," Statistical Papers, Springer, vol. 56(1), pages 61-82, February.
    4. Gonzalez-Rodriguez, Gil & Colubi, Ana & Angeles Gil, Maria, 2006. "A fuzzy representation of random variables: An operational tool in exploratory analysis and hypothesis testing," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 163-176, November.
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