lupmf</code>
versions of the functions cannot be defined directly (to do so will
produce an error). The difference in the
<code>_lpdf</code> and <code>_lpmf</code> and the corresponding <code>_lupdf</code> and <code>_lupmf</code> functions
is that if any other unnormalized density functions are used
inside the user-defined function, the <code>_lpdf</code> and <code>_lpmf</code> forms of the
user-defined function will change these densities to be normalized.
The <code>_lupdf</code> and <code>_lupmf</code> fo