
A copula method can be used to describe the dependency structure between several randomvariables. Copula methods are used widely in various research fields across different disciplines,ranging from finance to the bio-geophysical sciences (Dißmann et al., 2013; Klein et al.,2020; Mitskopoulos et al., 2022). While some other multivariate distributions, for instance amultivariate normal distribution, allow for a highly symmetric dependency structure with thesame univariate and multivariate marginal distributions, copulas can model the joint distributionof multiple random variables separately from their marginal distribution (Czado & Nagler,2021; Sklar, 1959).Once a copula distribution has been modelled, they allow for random samples of the data tobe generated, as well as conditional samples. For example, if a copula has been fit betweenpeople’s height and weight, this copula can create random correlated samples of both variablesas well as conditional samples, e.g., samples of weight given a specific height.Although copulas are an excellent tool to model dependencies in bivariate data, data with twovariables, there are only a limited number of copulas capable of modelling larger multivariatedatasets, for example, the Gaussian and Student-t copula. However, when modelling thedependencies between a large number of different variables, a more flexible multivariatemodelling tool may be required that does not assume a single copula to capture all theindividual dependencies. To this end, vine copulas have been proposed as a method toconstruct a multivariate model with the use of bivariate copulas as building blocks (Aas et al.,2009; Bedford & Cooke, 2001, 2002; Joe, 1997).In the previous example related to height and weight, a vine copula could be used to also modelage in relation to height and weight. Like bivariate copulas, vine copulas allow the user togenerate random and conditional samples (Cooke et al., 2015). However, to draw conditionalsamples from a vine copula for a specific variable, the vine copula has to be structured in sucha way that the order in which the samples are generated draws the variable of interest last,i.e. the sample is conditioned on the preceding samples of other variables. For example, if onewants to generate a conditional sample of height, the samples of age and weight have to beprovided first. Additionally, while it is more common to use copulas for continuous data, suchas weight and height, methods have been developed to also allow for discrete data, such asage, to be modelled (Mitskopoulos et al., 2022).VineCopulas is a Python package that is able to fit and simulate both bivariate and vinecopulas. This package allows for both discrete as well as continuous input data, and can drawconditional samples for any variables of interest with the use of different vine structures.
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