Correlation-based and-operations can be copulas : a proof

Miralles-Dolz, Enrique and Gray, Ander and Patelli, Edoardo and Ferson, Scott and Kreinovich, Vladik and Kosheleva, Olga (2023) Correlation-based and-operations can be copulas : a proof. Other. arXiv, Ithaca, NY. (https://doi.org/10.48550/arXiv.2301.05507)

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Abstract

In many practical situations, we know the probabilities a and b of two events A and B, and we want to estimate the joint probability Prob(A & B). The algorithm that estimates the joint probability based on the known values a and b is called an and-operation. An important case when such a reconstruction is possible is when we know the correlation between A and B; we call the resulting and-operation correlation-based. On the other hand, in statistics, there is a widely used class of and-operations known as copulas. Empirical evidence seems to indicate that the correlation-based and-operation derived in https://doi.org/10.1007/978-3-031-08971-8_64 is a copula, but until now, no proof of this statement was available. In this paper, we provide such a proof.

ORCID iDs

Miralles-Dolz, Enrique, Gray, Ander, Patelli, Edoardo ORCID logoORCID: https://orcid.org/0000-0002-5007-7247, Ferson, Scott, Kreinovich, Vladik and Kosheleva, Olga;
CORE (COnnecting REpositories)