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

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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.

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Funding

This study was funded by Golestan University (Grant Number 1213565/13).

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Authors and Affiliations

  1. Department of Statistics, Faculty of Science, Golestan University, Gorgan, 49138-15739, Iran

    Vahid Ranjbar

  2. Department of Statistics, Payame Noor University, Tehran, 19395-3697, Iran

    Gholamreza Hesamian

Authors
  1. Vahid Ranjbar
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  2. Gholamreza Hesamian
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Correspondence to Vahid Ranjbar.

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This article does not contain any studies with human participants performed by any of the authors.

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Ranjbar, V., Hesamian, G. Copula function for fuzzy random variables: applications in measuring association between two fuzzy random variables. Stat Papers 61, 503–522 (2020). https://doi.org/10.1007/s00362-017-0944-2

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