The paper Microfacet Models for Refraction through Rough Surfaces, page 3 section 3.1, describes the NDF.
The problem: Given incident ray v I'd like to generate a CDF F that given an angle θ gives the probability that normals are distributed at or less than θ from v, i.e. dot(v,m)<=cos(θ) w.p. F(θ).
For v = n where n is the macrosurface normal this is simple (Assuming isotropic NDF):
Which is very easy to compute for the common GGX or Beckmann NDFs.
The paper gives the formula 
but it is harder to integrate and still not useful.
Any help would be appreciated.
