integer parameters/variates can take real values in density/mass functions

Description

Functions such as binomial_lpmf never check that their size (N) and number of success (n) parameters have integer value types. This also applies to hypergeometric_lpmf and others.

As written, they'll merrily accept real values and return nonsensical results.

In the past, we've just assumed nobody would call them with real values because we define the acceptable signatures in the Stan language.

It would be better to enforce integer base value types for these arguments. This can be done with something like the following template parameter to ensure all of T1, T2, and T3 have integer value types:

typename = std::enable_if_t<std::is_integral<scalar_type_t<T1>>::value
                            && std::is_integral<scalar_type_t<T2>>::value
                            && std::is_integral<scalar_type_t<T3>>::value>

The doc also needs to indicate this won't work. I don't know a good way to test that integer instantiations don't compile.

Current Version:

v3.1.0

Start with the binomial_lpmf and hypergeometric_lpmf entry points and inspect their template signatures and documentation, then identify the other probability functions with the same issue. Done means integer-valued parameters remain supported, real-valued arguments are rejected, and the documentation states this restriction.