build based on 815dc84

dev/archimedeans/index.html

@@ -6,4 +6,4 @@
 ϕ⁻¹(C::MyAC{d},x)
 τ(C::MyAC{d})
 τ⁻¹(::MyAC{d},τ)
-radial_dist(C::MyAC{d})</code></pre><h1 id="Available-Archimedean-copulas"><a class="docs-heading-anchor" href="#Available-Archimedean-copulas">Available Archimedean copulas</a><a id="Available-Archimedean-copulas-1"></a><a class="docs-heading-anchor-permalink" href="#Available-Archimedean-copulas" title="Permalink"></a></h1><h2 id="Independence"><a class="docs-heading-anchor" href="#Independence">Independence</a><a id="Independence-1"></a><a class="docs-heading-anchor-permalink" href="#Independence" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-binding" id="Copulas.IndependentCopula" href="#Copulas.IndependentCopula"><code>Copulas.IndependentCopula</code></a> — <span class="docstring-category">Type</span></header><section><div><p>IndependentCopula{d,T}</p><p>Constructor</p><pre><code class="nohighlight hljs">IndependentCopula(d, θ)</code></pre><p>The <a href="https://en.wikipedia.org/wiki/Copula_(probability_theory)#Most_important_Archimedean_copulas">Independant Copula</a> in dimension <span>$d$</span> is the simplest copula, that has the form : </p><p class="math-container">\[C(\mathbf{x}) = \prod_{i=1}^d x_i.\]</p><p>It happends to be an Archimedean Copula, with generator : </p><p class="math-container">\[\phi(t) = \exp{-t}\]</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/lrnv/Copulas.jl/blob/b5e48b05336f14bcbe0a1f8b1481275f89e382b2/src/ArchimedeanCopulas/IndependentCopula.jl#L1-L20">source</a></section></article><h2 id="Clayton"><a class="docs-heading-anchor" href="#Clayton">Clayton</a><a id="Clayton-1"></a><a class="docs-heading-anchor-permalink" href="#Clayton" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-binding" id="Copulas.ClaytonCopula" href="#Copulas.ClaytonCopula"><code>Copulas.ClaytonCopula</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">ClaytonCopula{d,T}</code></pre><p>Fields:</p><ul><li>θ::Real - parameter</li></ul><p>Constructor</p><pre><code class="nohighlight hljs">ClaytonCopula(d, θ)</code></pre><p>The <a href="https://en.wikipedia.org/wiki/Copula_(probability_theory)#Most_important_Archimedean_copulas">Clayton</a> copula in dimension <span>$d$</span> is parameterized by <span>$\theta \in [-1,\infty)$</span> when <span>$d=2$</span> and <span>$\theta \in [0,\infty)$</span> if <span>$d&gt;2$</span>. It is an Archimedean copula with generator : </p><p class="math-container">\[\phi(t) = \left(1+\mathrm{sign}(\theta)*t\right)^{-1\frac{1}{\theta}}\]</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/lrnv/Copulas.jl/blob/b5e48b05336f14bcbe0a1f8b1481275f89e382b2/src/ArchimedeanCopulas/ClaytonCopula.jl#L1-L16">source</a></section></article><h2 id="Frank"><a class="docs-heading-anchor" href="#Frank">Frank</a><a id="Frank-1"></a><a class="docs-heading-anchor-permalink" href="#Frank" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-binding" id="Copulas.FrankCopula" href="#Copulas.FrankCopula"><code>Copulas.FrankCopula</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">FrankCopula{d,T}</code></pre><p>Fields:</p><ul><li>θ::Real - parameter</li></ul><p>Constructor</p><pre><code class="nohighlight hljs">FrankCopula(d, θ)</code></pre><p>The <a href="https://en.wikipedia.org/wiki/Copula_(probability_theory)#Most_important_Archimedean_copulas">Frank</a> copula in dimension <span>$d$</span> is parameterized by <span>$\theta \in [0,\infty)$</span>. It is an Archimedean copula with generator : </p><p class="math-container">\[\phi(t) = -\frac{\log\left(1+e^{-t}(e^{-\theta-1})\right)}{	heta}\]</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/lrnv/Copulas.jl/blob/b5e48b05336f14bcbe0a1f8b1481275f89e382b2/src/ArchimedeanCopulas/FrankCopula.jl#L1-L16">source</a></section></article><h2 id="Gumbel"><a class="docs-heading-anchor" href="#Gumbel">Gumbel</a><a id="Gumbel-1"></a><a class="docs-heading-anchor-permalink" href="#Gumbel" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-binding" id="Copulas.GumbelCopula" href="#Copulas.GumbelCopula"><code>Copulas.GumbelCopula</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">GumbelCopula{d,T}</code></pre><p>Fields:</p><ul><li>θ::Real - parameter</li></ul><p>Constructor</p><pre><code class="nohighlight hljs">GumbelCopula(d, θ)</code></pre><p>The <a href="https://en.wikipedia.org/wiki/Copula_(probability_theory)#Most_important_Archimedean_copulas">Gumbel</a> copula in dimension <span>$d$</span> is parameterized by <span>$\theta \in [1,\infty)$</span>. It is an Archimedean copula with generator : </p><p class="math-container">\[\phi(t) = \exp{-t^{\frac{1}{θ}}}\]</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/lrnv/Copulas.jl/blob/b5e48b05336f14bcbe0a1f8b1481275f89e382b2/src/ArchimedeanCopulas/GumbelCopula.jl#L1-L16">source</a></section></article><h2 id="Ali-Mikhail-Haq"><a class="docs-heading-anchor" href="#Ali-Mikhail-Haq">Ali-Mikhail-Haq</a><a id="Ali-Mikhail-Haq-1"></a><a class="docs-heading-anchor-permalink" href="#Ali-Mikhail-Haq" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-binding" id="Copulas.AMHCopula" href="#Copulas.AMHCopula"><code>Copulas.AMHCopula</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">AMHCopula{d,T}</code></pre><p>Fields:</p><ul><li>θ::Real - parameter</li></ul><p>Constructor</p><pre><code class="nohighlight hljs">AMHCopula(d, θ)</code></pre><p>The <a href="https://en.wikipedia.org/wiki/Copula_(probability_theory)#Most_important_Archimedean_copulas">AMH</a> copula in dimension <span>$d$</span> is parameterized by <span>$\theta \in [0,1)$</span>. It is an Archimedean copula with generator : </p><p class="math-container">\[\phi(t) = 1 - \frac{1-\theta}{e^{-t}-\theta}\]</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/lrnv/Copulas.jl/blob/b5e48b05336f14bcbe0a1f8b1481275f89e382b2/src/ArchimedeanCopulas/AMHCopula.jl#L1-L16">source</a></section></article><h2 id="Joe"><a class="docs-heading-anchor" href="#Joe">Joe</a><a id="Joe-1"></a><a class="docs-heading-anchor-permalink" href="#Joe" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-binding" id="Copulas.JoeCopula" href="#Copulas.JoeCopula"><code>Copulas.JoeCopula</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">JoeCopula{d,T}</code></pre><p>Fields:</p><ul><li>θ::Real - parameter</li></ul><p>Constructor</p><pre><code class="nohighlight hljs">JoeCopula(d, θ)</code></pre><p>The <a href="https://en.wikipedia.org/wiki/Copula_(probability_theory)#Most_important_Archimedean_copulas">Joe</a> copula in dimension <span>$d$</span> is parameterized by <span>$\theta \in [1,\infty)$</span>. It is an Archimedean copula with generator : </p><p class="math-container">\[\phi(t) = 1 - \left(1 - e^{-t}\right)^{\frac{1}{\theta}}\]</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/lrnv/Copulas.jl/blob/b5e48b05336f14bcbe0a1f8b1481275f89e382b2/src/ArchimedeanCopulas/JoeCopula.jl#L1-L16">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../ellipticals/">« Elliptical Copulas</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.12 on <span class="colophon-date" title="Thursday 26 October 2023 15:53">Thursday 26 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+radial_dist(C::MyAC{d})</code></pre><h1 id="Available-Archimedean-copulas"><a class="docs-heading-anchor" href="#Available-Archimedean-copulas">Available Archimedean copulas</a><a id="Available-Archimedean-copulas-1"></a><a class="docs-heading-anchor-permalink" href="#Available-Archimedean-copulas" title="Permalink"></a></h1><h2 id="Independence"><a class="docs-heading-anchor" href="#Independence">Independence</a><a id="Independence-1"></a><a class="docs-heading-anchor-permalink" href="#Independence" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-binding" id="Copulas.IndependentCopula" href="#Copulas.IndependentCopula"><code>Copulas.IndependentCopula</code></a> — <span class="docstring-category">Type</span></header><section><div><p>IndependentCopula{d,T}</p><p>Constructor</p><pre><code class="nohighlight hljs">IndependentCopula(d, θ)</code></pre><p>The <a href="https://en.wikipedia.org/wiki/Copula_(probability_theory)#Most_important_Archimedean_copulas">Independant Copula</a> in dimension <span>$d$</span> is the simplest copula, that has the form : </p><p class="math-container">\[C(\mathbf{x}) = \prod_{i=1}^d x_i.\]</p><p>It happends to be an Archimedean Copula, with generator : </p><p class="math-container">\[\phi(t) = \exp{-t}\]</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/lrnv/Copulas.jl/blob/815dc84674a3634292a44e6d78ebd360d085a841/src/ArchimedeanCopulas/IndependentCopula.jl#L1-L20">source</a></section></article><h2 id="Clayton"><a class="docs-heading-anchor" href="#Clayton">Clayton</a><a id="Clayton-1"></a><a class="docs-heading-anchor-permalink" href="#Clayton" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-binding" id="Copulas.ClaytonCopula" href="#Copulas.ClaytonCopula"><code>Copulas.ClaytonCopula</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">ClaytonCopula{d,T}</code></pre><p>Fields:</p><ul><li>θ::Real - parameter</li></ul><p>Constructor</p><pre><code class="nohighlight hljs">ClaytonCopula(d, θ)</code></pre><p>The <a href="https://en.wikipedia.org/wiki/Copula_(probability_theory)#Most_important_Archimedean_copulas">Clayton</a> copula in dimension <span>$d$</span> is parameterized by <span>$\theta \in [-1,\infty)$</span> when <span>$d=2$</span> and <span>$\theta \in [0,\infty)$</span> if <span>$d&gt;2$</span>. It is an Archimedean copula with generator : </p><p class="math-container">\[\phi(t) = \left(1+\mathrm{sign}(\theta)*t\right)^{-1\frac{1}{\theta}}\]</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/lrnv/Copulas.jl/blob/815dc84674a3634292a44e6d78ebd360d085a841/src/ArchimedeanCopulas/ClaytonCopula.jl#L1-L16">source</a></section></article><h2 id="Frank"><a class="docs-heading-anchor" href="#Frank">Frank</a><a id="Frank-1"></a><a class="docs-heading-anchor-permalink" href="#Frank" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-binding" id="Copulas.FrankCopula" href="#Copulas.FrankCopula"><code>Copulas.FrankCopula</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">FrankCopula{d,T}</code></pre><p>Fields:</p><ul><li>θ::Real - parameter</li></ul><p>Constructor</p><pre><code class="nohighlight hljs">FrankCopula(d, θ)</code></pre><p>The <a href="https://en.wikipedia.org/wiki/Copula_(probability_theory)#Most_important_Archimedean_copulas">Frank</a> copula in dimension <span>$d$</span> is parameterized by <span>$\theta \in [0,\infty)$</span>. It is an Archimedean copula with generator : </p><p class="math-container">\[\phi(t) = -\frac{\log\left(1+e^{-t}(e^{-\theta-1})\right)}{	heta}\]</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/lrnv/Copulas.jl/blob/815dc84674a3634292a44e6d78ebd360d085a841/src/ArchimedeanCopulas/FrankCopula.jl#L1-L16">source</a></section></article><h2 id="Gumbel"><a class="docs-heading-anchor" href="#Gumbel">Gumbel</a><a id="Gumbel-1"></a><a class="docs-heading-anchor-permalink" href="#Gumbel" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-binding" id="Copulas.GumbelCopula" href="#Copulas.GumbelCopula"><code>Copulas.GumbelCopula</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">GumbelCopula{d,T}</code></pre><p>Fields:</p><ul><li>θ::Real - parameter</li></ul><p>Constructor</p><pre><code class="nohighlight hljs">GumbelCopula(d, θ)</code></pre><p>The <a href="https://en.wikipedia.org/wiki/Copula_(probability_theory)#Most_important_Archimedean_copulas">Gumbel</a> copula in dimension <span>$d$</span> is parameterized by <span>$\theta \in [1,\infty)$</span>. It is an Archimedean copula with generator : </p><p class="math-container">\[\phi(t) = \exp{-t^{\frac{1}{θ}}}\]</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/lrnv/Copulas.jl/blob/815dc84674a3634292a44e6d78ebd360d085a841/src/ArchimedeanCopulas/GumbelCopula.jl#L1-L16">source</a></section></article><h2 id="Ali-Mikhail-Haq"><a class="docs-heading-anchor" href="#Ali-Mikhail-Haq">Ali-Mikhail-Haq</a><a id="Ali-Mikhail-Haq-1"></a><a class="docs-heading-anchor-permalink" href="#Ali-Mikhail-Haq" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-binding" id="Copulas.AMHCopula" href="#Copulas.AMHCopula"><code>Copulas.AMHCopula</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">AMHCopula{d,T}</code></pre><p>Fields:</p><ul><li>θ::Real - parameter</li></ul><p>Constructor</p><pre><code class="nohighlight hljs">AMHCopula(d, θ)</code></pre><p>The <a href="https://en.wikipedia.org/wiki/Copula_(probability_theory)#Most_important_Archimedean_copulas">AMH</a> copula in dimension <span>$d$</span> is parameterized by <span>$\theta \in [0,1)$</span>. It is an Archimedean copula with generator : </p><p class="math-container">\[\phi(t) = 1 - \frac{1-\theta}{e^{-t}-\theta}\]</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/lrnv/Copulas.jl/blob/815dc84674a3634292a44e6d78ebd360d085a841/src/ArchimedeanCopulas/AMHCopula.jl#L1-L16">source</a></section></article><h2 id="Joe"><a class="docs-heading-anchor" href="#Joe">Joe</a><a id="Joe-1"></a><a class="docs-heading-anchor-permalink" href="#Joe" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-binding" id="Copulas.JoeCopula" href="#Copulas.JoeCopula"><code>Copulas.JoeCopula</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">JoeCopula{d,T}</code></pre><p>Fields:</p><ul><li>θ::Real - parameter</li></ul><p>Constructor</p><pre><code class="nohighlight hljs">JoeCopula(d, θ)</code></pre><p>The <a href="https://en.wikipedia.org/wiki/Copula_(probability_theory)#Most_important_Archimedean_copulas">Joe</a> copula in dimension <span>$d$</span> is parameterized by <span>$\theta \in [1,\infty)$</span>. It is an Archimedean copula with generator : </p><p class="math-container">\[\phi(t) = 1 - \left(1 - e^{-t}\right)^{\frac{1}{\theta}}\]</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/lrnv/Copulas.jl/blob/815dc84674a3634292a44e6d78ebd360d085a841/src/ArchimedeanCopulas/JoeCopula.jl#L1-L16">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../ellipticals/">« Elliptical Copulas</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.12 on <span class="colophon-date" title="Thursday 26 October 2023 15:57">Thursday 26 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>