statslib_docs_invwish.html

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                <a data-toggle="collapse" href="#collapse1"><h4><strong style="font-size: 120%;">StatsLib: Inverse-Wishart Distribution</strong></h4></a>
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                    <a href="#intro">Introduction</a> <br>
                    <a href="#density">Density</a> <br>
                    <a href="#random">Random Sampling</a>
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<h3 style="text-align: left;" id="intro"><strong style="font-size: 120%;">Introduction</strong></h3>

<p>The density function of the inverse-Wishart distribution:</p>
$$
    f(\mathbf{X}; \boldsymbol{\Psi}, \nu) = \dfrac{|\boldsymbol{\Psi}|^{\frac{\nu}{2}}}{2^{\frac{\nu p}{2}} \Gamma_p\left( \frac{\nu}{2} \right)} | \mathbf{X} |^{-\frac{\nu + p + 1}{2}} \exp \left( - \frac{1}{2} \text{tr} (\boldsymbol{\Psi} \mathbf{X}^{-1}) \right)
$$
<p>where $\Gamma_p$ is the multivariate gamma function.</p>

<p>Parameters:</p>
<ul>
    <li><code>Psi_par</code> is $\boldsymbol{\Psi}$</li>
    <li><code>nu_par</code> is $\nu$</li>
</ul>

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<h3 style="text-align: left;" id="density"><strong style="font-size: 120%;">Density</strong></h3>

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<p><strong>Definition:</strong></p>
<pre class="brush: cpp;">
template&lt;typename mT, typename pT&gt;
statslib_inline
return_t&lt;pT&gt; dinvwish(const mT& X, const mT& Psi_par, const pT nu_par, bool log_form = false);
</pre>

<p>Computes the density function.</p>

<hr>

<p><strong>Examples:</strong></p>
<pre class="brush: cpp;">
// parameters
arma::mat Psi = arma::eye(5,5);
double nu = 10.0;

// Armadillo input
arma::mat X(10,1);
X.fill(2.5);

arma::mat dens_vals_mat = stats::dinvwish(X,Psi,nu);
arma::mat log_dens_vals_mat = stats::dinvwish(X,Psi,nu,true);
</pre>

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<h3 style="text-align: left;" id="random"><strong style="font-size: 120%;">Random Sampling</strong></h3>

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<p><strong>Definition:</strong></p>
<pre class="brush: cpp;"> 
template&lt;typename mT, typename pT&gt;
statslib_inline
mT rinvwish(const mT& Psi_par, const pT nu_par, const bool pre_chol = false);
</pre>

<p>Generates pseudo-random draws.</p>

<p>Here <code>pre_chol</code> indicates whether <code>Psi_par</code> is being passed as a Cholesky decomposition (in <strong>lower triangular</strong> format).</p>

<hr>

<p><strong>Examples:</strong></p>
<pre class="brush: cpp;">
// parameters
arma::mat Psi = arma::eye(5,5);
double nu = 10.0;

// Armadillo output
arma::mat rand_mat = stats::rinvwish&lt;arma::mat&gt;(Psi,nu);
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