Beta cdf/lcdf/lccdf prob tests wrong

[bbbales2]

Description

The cdf_function is supposed to be a reference implementation (see the exponential version as an example).

The beta distribution in Stan is just testing against itself:
https://github.com/stan-dev/math/blob/develop/test/prob/beta/beta_cdf_test.hpp
https://github.com/stan-dev/math/blob/develop/test/prob/beta/beta_cdf_log_test.hpp
https://github.com/stan-dev/math/blob/develop/test/prob/beta/beta_cdf_log_test.hpp

I'm not sure of the value of a lot of the reference implementations in the test framework (I assume they're just copied from early implementations in the library), but this is still a bit of a blindspot in the tests.

Current Version:

v3.2.0

[bob-carpenter]

I'm not sure of the value of a lot of the reference implementations in the test framework

The motivation was that it was easier to write a sound version of normal that operates on scalars and use that to test the vectorized form. I have no idea where things stand now that there's a testing framework.

[bbbales2]

easier to write a sound version of normal that operates on scalars

That makes sense, so even if it is basically the same code, it's still helping us weed out vectorization problems.

[bob-carpenter]

It wasn't the same code. The distributions all use operands and partials, right? But the simple implementations were simple and just autodiffed through the functions. It's also a convenient way to test any autodiff. Write a simple version of a function, then test autodiffing that vs. the one with custom autodiff.

[bbbales2]

The distributions all use operands and partials, right? But the simple implementations were simple and just autodiffed through the functions.

Oh interesting, I didn't know that was true for all the pdf/cdfs. I suppose we should be doing ops and partials for the Von Mises CDF then as well.