CDFs for discrete variables and PMFs only allow integer values

Description

Functions such as bernoulli_cdf and bernoulli_pmf only accept integer values. This is mathematically imprecise, as CDFs and PMFs should be defined for all real numbers (e.g., pbinom and dbinom in R accept non-integer values).

This is a problem, e.g., if you have a matrix Y of values where each column has a different distribution (e.g., first column is Gaussian, second column is Bernoulli). Such constructs are necessary to create a general Gaussian copula function.

Example

binomial_cdf(0.5, 0.75);

Expected Output

0.25

Currently, no code will compile if a non-integer value is input as the first argument to binomial_cdf(0.5, 0.75).

Current Version:

v4.0.1

Start by locating the C++ implementations and tests for bernoulli_cdf, bernoulli_pmf, and binomial_cdf. Inspect how the first argument's type is constrained, then identify the other discrete CDF and PMF functions that need the same treatment. Done means binomial_cdf(0.5, 0.75) compiles and returns 0.25, with tests covering the updated behavior.