Correlation-Based And-Operations Can Be Copulas: A Proof

01/13/2023

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by   Enrique Miralles-Dolz, et al.

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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.