=
\left( 1 - \sum_{k&#39;=1}^{k-1} x_{k&#39;} \right) z_k.
\]</span></p>
<p>The summation term represents the length of the original stick left at
stage <span class="math inline">\(k\)</span>. This is multiplied by the break proportion <span class="math inline">\(z_k\)</span> to yield
<span class="math inline">\(x_k\)</span>. Only <span class="math inline">\(K-1\)</span> unconstrained parameters are required, with
the last dimension’s value <span class="math inline">\(x_K\)</span> set to the length of the