Copulas.jl: A fully Distributions.jl-compliant copula package

Abstract

Copulas are functions that describe dependence structures of random vectors, without describing their univariate marginals. In statistics, the separation is sometimes useful, the quality and/or quantity of available information on these two objects might differ. This separation can be formally stated through Sklar's theorem. Copulas are standard tools in probability and statistics, with a wide range of applications from biostatistics, finance or medicine, to fuzzy logic, global sensitivity and broader analysis. The Julia package \texttt{Copulas.jl} brings most standard copula-related features into native Julia: random number generation, density and distribution function evaluations, fitting, construction of multivariate models through Sklar's theorem, and many more related functionalities. Copulas being fundamentally distributions of random vectors, we fully comply with the \texttt{Distributions.jl} API, the Julian standard for implementation of random variables and random vectors. This compliance allows interoperability with other packages based on this API such as, e.g., \texttt{Turing.jl} and several others.

References in corpus (5)

• Multivariate Archimedean copulas, $d$-monotone functions and ${\ell }_1$-norm symmetric distributions
• Distributions.jl: Definition and Modeling of Probability Distributions in the JuliaStats Ecosystem
• Robust benchmarking in noisy environments
• Introducing higher order correlations to marginals' subset of multivariate data by means of Archimedean copulas
• Selected Methods for non-Gaussian Data Analysis