lue <span class="math inline">\(b\)</span>. If we were interested in calculating the expectation of a variable <span class="math inline">\(X\)</span> distributed in this way, we would need to calculate <span class="math display">\[
\int_a^b xf(x)\,dx = \int_{\delta}^b xf(x)\,dx
\]</span> in the numerator, where <span class="math inline">\(f(x)\)</span> is the probability density function for the shifted log-normal distribution. This probability density function can be coded in Stan as:</p>
<div class="sourc