r every custom <code>_lpdf</code> and <code>_lpmf</code> defined there is a corresponding <code>_lupdf</code> and <code>_lupmf</code> defined automatically. The <code>_lupdf</code> and <code>_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-def