he pdf of a beta distribution when the values of <span class="math inline">\(\alpha\)</span> and <span class="math inline">\(\beta\)</span> are small, most of the probability mass is lumped near zero and one.</p>
<p>The pdf of a beta distribution is proportional to</p>
<p><span class="math display">\[
p(x) \propto x^{\alpha - 1}(1 - x)^{\beta - 1}
\]</span></p>
<p>Normalizing this distribution requires computing the integral of <span class="math inline">\(p(x)\)</span> from zero to one. In Stan code, the in