diff --git a/docs/make.jl b/docs/make.jl index 478f65eb..2e6573e8 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -26,8 +26,7 @@ makedocs(; "Getting Started" => "getting_started.md", "Sklar's Distributions" => "sklar.md", "Elliptical Copulas" => "elliptical/generalities.md", - "Archimedean Copulas" => "archimedean/generalities.md", - "Liouville Copulas" => "Liouville.md", + "Archimedean Generators" => "archimedean/generalities.md", "Extreme Value Copulas" => "extremevalue/generalities.md", "Empirical Copulas" => "empirical/generalities.md", "Vines Copulas" => "Vines.md", diff --git a/docs/src/Liouville.md b/docs/src/Liouville.md deleted file mode 100644 index 50453f64..00000000 --- a/docs/src/Liouville.md +++ /dev/null @@ -1,21 +0,0 @@ -```@meta -CurrentModule = Copulas -``` - -# Liouville Copulas - -!!! todo "Not merged yet !" - Liouville copulas are coming in this PR : https://github.com/lrnv/Copulas.jl/pull/83, but the work is not finished. - -Archimedean copulas have been widely used in the literature due to their nice decomposition properties and easy parametrization. The interested reader can refer to the extensive literature [hofert2010,hofert2013a,mcneil2010,cossette2017,cossette2018,genest2011a,dibernardino2013a,dibernardino2013a,dibernardino2016,cooray2018,spreeuw2014](@cite) on Archimedean copulas, their nesting extensions and most importantly their estimation. - -One major drawback of the Archimedean family is that these copulas have exchangeable marginals (i.e., $C(\bm u) = C(\mathrm{p}(\bm u))$ for any permutation $p(\bm u)$ of $u_1,...,u_d$): the dependence structure is symmetric, which might not be a wanted property. However, from the Radial-simplex expression, we can easily extrapolate a little and take for $\bm S$ a non-uniform distribution on the simplex. - -Liouville's copulas share many properties with Archimedean copulas, but are not exchangeable anymore. This is an easy way to produce non-exchangeable dependence structures. See [cote2019](@cite) for a practical use of this property. - -Note that Dirichlet distributions are constructed as $\bm S = \frac{\bm G}{\langle \bm 1, \bm G\rangle}$, where $\bm G$ is a vector of independent Gamma distributions with unit scale (and potentially different shapes: taking all shapes equal yields the Archimedean case). - -```@bibliography -Pages = ["Liouville.md"] -Canonical = false -``` \ No newline at end of file diff --git a/docs/src/archimedean/generalities.md b/docs/src/archimedean/generalities.md index 0b36525f..9616e931 100644 --- a/docs/src/archimedean/generalities.md +++ b/docs/src/archimedean/generalities.md @@ -211,12 +211,27 @@ for which the corresponding distribution is known but has no particular name, th ArchimedeanCopula ``` - +# Liouville Copulas + +!!! todo "Not merged yet !" + Liouville copulas are coming in this PR : https://github.com/lrnv/Copulas.jl/pull/83, but the work is not finished. + +Archimedean copulas have been widely used in the literature due to their nice decomposition properties and easy parametrization. The interested reader can refer to the extensive literature [hofert2010,hofert2013a,mcneil2010,cossette2017,cossette2018,genest2011a,dibernardino2013a,dibernardino2013a,dibernardino2016,cooray2018,spreeuw2014](@cite) on Archimedean copulas, their nesting extensions and most importantly their estimation. + +One major drawback of the Archimedean family is that these copulas have exchangeable marginals (i.e., $C(\bm u) = C(\mathrm{p}(\bm u))$ for any permutation $p(\bm u)$ of $u_1,...,u_d$): the dependence structure is symmetric, which might not be a wanted property. However, from the Radial-simplex expression, we can easily extrapolate a little and take for $\bm S$ a non-uniform distribution on the simplex. + +Liouville's copulas share many properties with Archimedean copulas, but are not exchangeable anymore. This is an easy way to produce non-exchangeable dependence structures. See [cote2019](@cite) for a practical use of this property. + +Note that Dirichlet distributions are constructed as $\bm S = \frac{\bm G}{\langle \bm 1, \bm G\rangle}$, where $\bm G$ is a vector of independent Gamma distributions with unit scale (and potentially different shapes: taking all shapes equal yields the Archimedean case). + + + + ```@bibliography -Pages = ["generalities.md"] +Pages = [@__FILE__] Canonical = false ```