proach the upper limit of integration <span class="math inline">\(a = 1\)</span>, <code>xc</code> will take on the value of <span class="math inline">\(a - x = 1 - x\)</span>. This version of the integrand will converge for much smaller values of <code>alpha</code> and <code>beta</code> than otherwise possible.</p>
<p>Consider another example: let’s say we have a log-normal distribution that is both shifted away from zero by some amount <span class="math inline">\(\delta\)</span>, and truncated at some va