diff --git a/docs/make.jl b/docs/make.jl index 0f13293e..478f65eb 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -30,6 +30,7 @@ makedocs(; "Liouville Copulas" => "Liouville.md", "Extreme Value Copulas" => "extremevalue/generalities.md", "Empirical Copulas" => "empirical/generalities.md", + "Vines Copulas" => "Vines.md", "Dependence measures" => "dependence_measures.md", ], diff --git a/docs/src/Vines.md b/docs/src/Vines.md index 7bb5b31a..1a8c410b 100644 --- a/docs/src/Vines.md +++ b/docs/src/Vines.md @@ -1,5 +1,20 @@ +```@meta +CurrentModule = Copulas +``` -One more noticeable class of copulas are the Vines copulas. These distributions use a graph of conditional distributions to encode the distribution of the random vector. To define such a model, working with conditional densities, and given any ordered partition $\bm i_1,...\bm i_p$ of $1,...d$, we write: +# Vines Copulas + +!!! todo "Not implemented yet!" + Do not hesitate to come talk on [our GitHub](https://github.com/lrnv/Copulas.jl) ! + +One more noticeable class of copulas are the Vines copulas. These distributions use a graph of conditional distributions to encode the distribution of the random vector. To define such a model, working with conditional densities, and given any ordered partition $\bm i_1,...\bm i_p$ of $1,...d$, we write: + $$f(\bm x) = f(x_{\bm i_1}) \prod\limits_{j=1}^{p-1} f(x_{\bm i_{j+1}} | x_{\bm i_j}).$$ -Of course, the choice of the partition, of its order, and of the conditional models is left to the practitioner. The goal when dealing with such dependency graphs is to tailor the graph to reduce the error of approximation, which can be a tricky task. There exists simplifying assumptions that help with this matter, and we refer to ~\cite{durante2017a,nagler2016,nagler2018,czado2013,czado2019,graler2014} for a deep dive into the vine theory, along with some nice results and extensions. \ No newline at end of file +Of course, the choice of the partition, of its order, and of the conditional models is left to the practitioner. The goal when dealing with such dependency graphs is to tailor the graph to reduce the error of approximation, which can be a tricky task. There exists simplifying assumptions that help with this matter, and we refer to [durante2017a,nagler2016,nagler2018,czado2013,czado2019,graler2014](@cite) for a deep dive into the vine theory, along with some nice results and extensions. + + +```@bibliography +Pages = ["Liouville.md"] +Canonical = false +``` \ No newline at end of file