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-{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-22T08:04:09","documenter_version":"1.7.0"}}
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dev/elliptical/available_models/index.html

@@ -3,8 +3,8 @@
 Random.rand!(C,u) # other calling syntax for rng.
 pdf(C,u) # to get the density
 cdf(C,u) # to get the distribution function 
-Ĉ = fit(GaussianCopula,u) # to fit on the sampled data. </code></pre><p>GaussianCopulas have a special case: </p><ul><li>When <code>isdiag(Σ)</code>, the constructor returns an <code>IndependentCopula(d)</code></li></ul><p>References:</p><ul><li>[<a href="../../references/#nelsen2006">3</a>] Nelsen, Roger B. An introduction to copulas. Springer, 2006.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/lrnv/Copulas.jl/blob/b803ddfa348c5bd05d314acdb6497dcadc9303a2/src/EllipticalCopulas/GaussianCopula.jl#L1-L38">source</a></section></article><h2 id="TCopula"><a class="docs-heading-anchor" href="#TCopula"><code>TCopula</code></a><a id="TCopula-1"></a><a class="docs-heading-anchor-permalink" href="#TCopula" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Copulas.TCopula" href="#Copulas.TCopula"><code>Copulas.TCopula</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">TCopula{d,MT}</code></pre><p>Fields:</p><ul><li>df::Int - number of degree of freedom</li><li>Σ::MT - covariance matrix</li></ul><p>Constructor</p><pre><code class="nohighlight hljs">TCopula(df,Σ)</code></pre><p>The Student&#39;s <a href="https://en.wikipedia.org/wiki/Multivariate_t-distribution#Copulas_based_on_the_multivariate_t">T Copula</a> is the  copula of a <a href="https://en.wikipedia.org/wiki/Multivariate_t-distribution">Multivariate Student distribution</a>. It is constructed as : </p><p class="math-container">\[C(\mathbf{x}; \boldsymbol{n,\Sigma}) = F_{n,\Sigma}(F_{n,\Sigma,i}^{-1}(x_i),i\in 1,...d)\]</p><p>where <span>$F_{n,\Sigma}$</span> is a cdf of a multivariate student random vector with covariance matrix <span>$\Sigma$</span> and <span>$n$</span> degrees of freedom. and <code>F_{n,\Sigma,i}</code> is the ith marignal cdf. </p><p>It can be constructed in Julia via:  </p><pre><code class="language-julia hljs">C = TCopula(2,Σ)</code></pre><p>You can sample it, compute pdf and cdf, or even fit the distribution via: </p><pre><code class="language-julia hljs">u = rand(C,1000)
+Ĉ = fit(GaussianCopula,u) # to fit on the sampled data. </code></pre><p>GaussianCopulas have a special case: </p><ul><li>When <code>isdiag(Σ)</code>, the constructor returns an <code>IndependentCopula(d)</code></li></ul><p>References:</p><ul><li>[<a href="../../references/#nelsen2006">3</a>] Nelsen, Roger B. An introduction to copulas. Springer, 2006.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/lrnv/Copulas.jl/blob/0e3d81dc428029ee8963462237a5b42ad2e6a8f1/src/EllipticalCopulas/GaussianCopula.jl#L1-L38">source</a></section></article><h2 id="TCopula"><a class="docs-heading-anchor" href="#TCopula"><code>TCopula</code></a><a id="TCopula-1"></a><a class="docs-heading-anchor-permalink" href="#TCopula" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Copulas.TCopula" href="#Copulas.TCopula"><code>Copulas.TCopula</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">TCopula{d,MT}</code></pre><p>Fields:</p><ul><li>df::Int - number of degree of freedom</li><li>Σ::MT - covariance matrix</li></ul><p>Constructor</p><pre><code class="nohighlight hljs">TCopula(df,Σ)</code></pre><p>The Student&#39;s <a href="https://en.wikipedia.org/wiki/Multivariate_t-distribution#Copulas_based_on_the_multivariate_t">T Copula</a> is the  copula of a <a href="https://en.wikipedia.org/wiki/Multivariate_t-distribution">Multivariate Student distribution</a>. It is constructed as : </p><p class="math-container">\[C(\mathbf{x}; \boldsymbol{n,\Sigma}) = F_{n,\Sigma}(F_{n,\Sigma,i}^{-1}(x_i),i\in 1,...d)\]</p><p>where <span>$F_{n,\Sigma}$</span> is a cdf of a multivariate student random vector with covariance matrix <span>$\Sigma$</span> and <span>$n$</span> degrees of freedom. and <code>F_{n,\Sigma,i}</code> is the ith marignal cdf. </p><p>It can be constructed in Julia via:  </p><pre><code class="language-julia hljs">C = TCopula(2,Σ)</code></pre><p>You can sample it, compute pdf and cdf, or even fit the distribution via: </p><pre><code class="language-julia hljs">u = rand(C,1000)
 Random.rand!(C,u) # other calling syntax for rng.
 pdf(C,u) # to get the density
 cdf(C,u) # to get the distribution function 
-Ĉ = fit(TCopula,u) # to fit on the sampled data. </code></pre><p>Except that currently it does not work since <code>fit(Distributions.MvTDist,data)</code> does not dispatch. </p><p>References:</p><ul><li>[<a href="../../references/#nelsen2006">3</a>] Nelsen, Roger B. An introduction to copulas. Springer, 2006.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/lrnv/Copulas.jl/blob/b803ddfa348c5bd05d314acdb6497dcadc9303a2/src/EllipticalCopulas/TCopula.jl#L1-L39">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../dependence_measures/">« Dependence measures</a><a class="docs-footer-nextpage" href="../../archimedean/available_models/">Archimedean Generators »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Sunday 22 September 2024 08:04">Sunday 22 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+Ĉ = fit(TCopula,u) # to fit on the sampled data. </code></pre><p>Except that currently it does not work since <code>fit(Distributions.MvTDist,data)</code> does not dispatch. </p><p>References:</p><ul><li>[<a href="../../references/#nelsen2006">3</a>] Nelsen, Roger B. An introduction to copulas. Springer, 2006.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/lrnv/Copulas.jl/blob/0e3d81dc428029ee8963462237a5b42ad2e6a8f1/src/EllipticalCopulas/TCopula.jl#L1-L39">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../dependence_measures/">« Dependence measures</a><a class="docs-footer-nextpage" href="../../archimedean/available_models/">Archimedean Generators »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Sunday 22 September 2024 09:01">Sunday 22 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>