ven the break proportions
<span class="math inline">\(z\)</span>, <span class="math inline">\(y\)</span> is defined elementwise by</p>
<p><span class="math display">\[
y_k
= \mathrm{logit}(z_k)
- \mbox{log}\left(
   \frac{1}{K-k}
   \right)
.
\]</span></p>
<p>The break proportions <span class="math inline">\(z_k\)</span> are defined to be the ratio of <span class="math inline">\(x_k\)</span> to
the length of stick left after the first <span class="math inline">\(k-1\)</span> pieces have been broken
off,</p>