Add other exponential family members

[jtobin]

Currently missing:

• [x] negative binomial
• [x] pareto
• [x] weibull
• [x] laplace
• [x] chisquare
• [x] inverse gaussian
• [x] normal-gamma
• [ ] normal-inverse-gamma (requires code for the gamma function)

Multivariate

• [ ] multivariate normal

Matrix-valued

• [ ] wishart
• [ ] inverse-wishart

[ocramz]

In https://github.com/ocramz/sde I have implemented the symmetric Levy stable distribution, which gives the Laplace for alpha==1. Here's my code; the samples "look ok" but I haven't verified the results against known CDFs (apart from the Gaussian special case, alpha==2), so use it with caution.

alphaStable100 :: PrimMonad m => Double -> Prob m Double
alphaStable100 al = do
  u0 <- uniform
  w <- exponential 1
  let u = pi * u0 - 0.5 * pi                         -- uniform on (-pi/2, pi/2)
      t1 = sin (al * u)
      t2 = cos u**(-1/al)
      t3 = (cos ((al-1) * u) / w)**((1-al)/al)
      z = t1 * t2 * t3
  case al of 1 -> return $ tan u
             _ -> return z

[jtobin]

Thanks Marco, I'll take a look in a few days. Currently in Bali ringing in the new year - happy 2017! :smile:

[ocramz]

Here's to a smashing new year! All the best from Sweden!

[ocramz]

@jtobin Jared, I think the multivariate distributions need a good story for matrix algebra. Do you have any suggestions? I think adding hmatrix as a dependency here would be excessive, though. My own sparse-linear-algebra is still not ready for prime time, sadly