From 28a2ddef7099a29ade5319c909b9c284e953f6d7 Mon Sep 17 00:00:00 2001 From: Santiago Jimenez Ramos Date: Fri, 27 Oct 2023 10:01:24 -0300 Subject: [PATCH 1/2] Plackett copula documentation added --- src/MiscellaneousCopulas/PlackettCopula.jl | 20 ++++++++++++++++++++ 1 file changed, 20 insertions(+) diff --git a/src/MiscellaneousCopulas/PlackettCopula.jl b/src/MiscellaneousCopulas/PlackettCopula.jl index 02d2b2ec..010bb845 100644 --- a/src/MiscellaneousCopulas/PlackettCopula.jl +++ b/src/MiscellaneousCopulas/PlackettCopula.jl @@ -1,3 +1,23 @@ +""" + PlackettCopula{P} + +Fields: + - θ::Real - parameter + +Constructor + + PlackettCopula(θ) + +Parameterized by ``\\theta > 0, \\theta \\neq 1`` The [Plackett](https://www.cambridge.org/core/books/abs/copulas-and-their-applications-in-water-resources-engineering/plackett-copula/2D407DAB691623AB52CF74044B42C61F) copula is + +```math +\\C_{\\theta}(u,v) = \\frac{\\left [1+(\\theta-1)(u+v)\\right]- \\sqrt{[1+(\\theta-1)(u+v)]^2-4uv\\theta(\\theta-1)}}{2(\\theta-1)} +``` +and for ``\\theta = 1`` + ```math +\\C_{1}(u,v) = uv ``` + +""" #= Details about Plackett copulation are found in Joe, H. (2014). Dependence modeling with copulas. CRC press, Page.164 ==# From adf8ba296b0f6c34cded8dc0b2783b917f9db052 Mon Sep 17 00:00:00 2001 From: Oskar Laverny Date: Fri, 27 Oct 2023 16:42:43 +0200 Subject: [PATCH 2/2] move reference to joe --- src/MiscellaneousCopulas/PlackettCopula.jl | 6 +----- 1 file changed, 1 insertion(+), 5 deletions(-) diff --git a/src/MiscellaneousCopulas/PlackettCopula.jl b/src/MiscellaneousCopulas/PlackettCopula.jl index 010bb845..06fe9ff1 100644 --- a/src/MiscellaneousCopulas/PlackettCopula.jl +++ b/src/MiscellaneousCopulas/PlackettCopula.jl @@ -17,12 +17,8 @@ and for ``\\theta = 1`` ```math \\C_{1}(u,v) = uv ``` +More details about Plackett copulation are found in Joe, H. (2014). Dependence modeling with copulas. CRC press, Page.164 """ -#= Details about Plackett copulation are found in Joe, H. (2014). - Dependence modeling with copulas. CRC press, Page.164 -==# - -#Create an instance of the Plackett copula struct PlackettCopula{P} <: Copula{2} # since it is only bivariate. θ::P # Copula parameter