
<p><span class="math display">\[
x_k = y_1 + \sum_{k&#39;=2}^k \exp(y_{k&#39;}).
\]</span></p>
</div>
<div id="absolute-jacobian-determinant-of-the-ordered-inverse-transform" class="section level3 unnumbered">
<h3>Absolute Jacobian determinant of the ordered inverse transform</h3>
<p>The Jacobian of the inverse transform <span class="math inline">\(f^{-1}\)</span> is lower triangular,
with diagonal elements for <span class="math inline">\(1 \leq k \leq K\)</span> of</p>
<p><span class="math display">\[
J_{