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Abstract
We propose a copula-type representation for random couples with Bernoulli margins. Some dependence measures for binary data are re-examined. It is stressed that satisfactory dependence measure should only depend on the discrete copula, and not on the margins.
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Citations

Denuit, M., Lambert, P., & Tajar, A. (2001). Copula-type representation for random couples with Bernoulli margins (STAT Discussion Paper 0118). https://hdl.handle.net/2078.5/33591