Skip to content

Commit

Permalink
add the vines file to the docs
Browse files Browse the repository at this point in the history
  • Loading branch information
lrnv committed Sep 22, 2024
1 parent e035370 commit a575c78
Show file tree
Hide file tree
Showing 2 changed files with 18 additions and 2 deletions.
1 change: 1 addition & 0 deletions docs/make.jl
Original file line number Diff line number Diff line change
Expand Up @@ -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",
],

Expand Down
19 changes: 17 additions & 2 deletions docs/src/Vines.md
Original file line number Diff line number Diff line change
@@ -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.
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
```

0 comments on commit a575c78

Please sign in to comment.