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A copula is a multivariate distribution with uniform marginal distributions. Copulas are mostly used to represent or to model the structure of dependence between random variables, separately from the marginal distributions.

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Do any standard copulas fit well these sampled bivariate data--exhibiting repulsive behavior...

Corollary 1 in marginalinvariance]) that the ratio of Q1 to q1 constitutes a sample from a (symmetric) bivariate copula (alternatively termed "permutons or doubly-stochastic measures" WikiCopula) $f(x, … A Gaussian copula with uniform marginals over [0,1] would be quite appealing conceptually--due to the wide range of applicability of multivariate normal distributions. …
Paul B. Slater's user avatar
1 vote
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What are examples of symmetric copulas $f(x,y)=f(y,x)$ having relative minima for $f(x,x)$?

That is, based on my study BlochRadiiRepulsion, I believe that I am dealing with a symmetric copula $f(x,y)=f(y,x)$ defined over the unit square for which the values of $f(x,x)$ assume relative minima …
Paul B. Slater's user avatar
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Is a bivariate copula relevant in this physics setting manifesting uniform univariate margin...

Our question here is whether it is suitable--and how--to search in this setting for a bivariate copula having these two marginal uniform distributions. … This finding led us to the question what--if any--is the pertinent bivariate copula having this pair of uniform marginals. …
Paul B. Slater's user avatar