Related papers: A new family of smooth copulas with arbitrarily ir…
We introduce a new family of copula densities constructed from univariate distributions on $[0,1]$. Although our construction is structurally simple, the resulting family is versatile: it includes both smooth and irregular examples, and…
We propose a semiparametric family of copulas based on a set of orthonormal functions and a matrix. This new copula permits to reach values of Spearman's Rho arbitrarily close to one without introducing a singular component. Moreover, it…
Copulas are now frequently used to construct or estimate multivariate distributions because of their ability to take into account the multivariate dependence of the different variables while separately specifying marginal distributions.…
In this article, the concept of copulas is generalised to infinite dimensional Hilbert spaces. We show one direction of Sklar's theorem and explain that the other direction fails in infinite dimensional Hilbert spaces. We derive a necessary…
When scholars study joint distributions of multiple variables, copulas are useful. However, if the variables are not linearly correlated with each other yet are still not independent, most of conventional copulas are not up to the task.…
Nested Archimedean copulas recently gained interest since they generalize the well-known class of Archimedean copulas to allow for partial asymmetry. Sampling algorithms and strategies have been well investigated for nested Archimedean…
We propose reinterpreting copula density estimation as a discriminative task. Under this novel estimation scheme, we train a classifier to distinguish samples from the joint density from those of the product of independent marginals,…
In this paper, we investigate several subsets of $n$-copulas and $n$-quasi-copulas from the perspective of convex-lineability and the recently introduced concept of convex-spaceability. Our purpose is to determine when such families contain…
W-transforms are introduced as uniformity-preserving univariate transformations on the unit interval induced by distribution functions and piecewise strictly monotone functions, and their properties are investigated. When applied…
Multivariate distributions are fundamental to modeling. Discrete copulas can be used to construct diverse multivariate joint distributions over random variables from estimated univariate marginals. The space of discrete copulas admits a…
We introduce a family of copulas which are locally piecewise uniform in the interior of the unit cube of any given dimension. Within that family, the simultaneous control of tail dependencies of all projections to faces of the cube is…
We explore whether observed molecular clouds could include a substantial population of unbound clouds. Using simulations which include only turbulence and gravity, we are able to match observed relations and naturally reproduce the observed…
Copula modelling has become ubiquitous in modern statistics. Here, the problem of nonparametrically estimating a copula density is addressed. Arguably the most popular nonparametric density estimator, the kernel estimator is not suitable…
We investigate the asymptotic properties of random polytopes arising as convex hulls of $n$ independent random points sampled from a family of block-beta distributions. Notably, this family includes the uniform distribution on a product of…
The characterizations when two natural upper bounds of the set of copulas with a given diagonal section are copulas have been well studied in the literature. Given a curvilinear section, however, there is only a partial result concerning…
Copulas allow a flexible and simultaneous modeling of complicated dependence structures together with various marginal distributions. Especially if the density function can be represented as the product of the marginal density functions and…
In this paper we study nonparametric estimators of copulas and copula densities. We first focus our study on a density copula estimator based on a polynomial orthogonal projection of the joint density. A new copula estimator is then…
We give a number of results about families of Ulam sets. Generalizing behavior of Ulam sets U(1,n), we prove using an novel model theoretic approach that there is a rigidity phenomenon for Ulam sets U(a,b) as b increases. Based on this, we…
The large scale distribution of galaxies in the universe displays a complex pattern of clusters, super-clusters, filaments and voids with sizes limited only by the boundaries of the available samples. A quantitative statistical…
A new method for constructing absolutely continuous two--dimensional copulas by differential equations is presented. The copulas are symmetric with respect to reflection in the opposite diagonal. The support of the copula density may be…