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

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:Theorem: existence and uniqueness of the copula (Sklar, 1959): For a given -variate absolutely continuous random vector X with marginals 1 , ... , there exists a unique function , the copula, such thatwhere , 1 , ... are respectively the distributions functions of X, 1 , ... .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.A few standard theoretical references on the matter are Joe (1997), Nelsen (2006), Joe (2014), and Durante & Sempi (2015).The Julia package Copulas.jlbrings 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.Since copulas can combine arbitrary univariate distributions to form distributions of multivariate random vectors, we fully comply with the Distributions.jlAPI (Besançon et al., 2021;Lin et al., 2019), 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., Turing.jl(Ge et al., 2018) and several others.