nction
directly implementing <span class="math inline">\(f(x) = \log (1 + x)\)</span>. In Stan (as in C++),
this operation is written as <code>log1p(x)</code>. Because <code>x</code> itself may be
close to zero, the function <code>log1p(x)</code> can take the logarithm of
values very close to one, the results of which are close to zero.</p>
<p>Similarly, the complementary cumulative distribution functions (CCDF),
defined by <span class="math inline">\(F^{\complement}_Y(y) = 1 - F_Y(y)\)</span>, where <span 