Math formulas in Haskell

Question

I wrote some math formulas in Haskell and was wondering about how to clean the code up and make it more readable.

import Math.Gamma

pdf :: Double -> Double -> Double -> Double -> Double
pdf mu alpha beta x =
    ( beta / (2 * alpha * gamma  ( 1/beta) ) ) **
    exp ( -1* ( abs(x - mu )/alpha )) ** beta

cdf :: Double -> Double -> Double -> Double -> Double
cdf mu alpha beta x = 0.5 + signum(x - mu) * ( lowerGamma  (1/beta) ((abs(x-mu) / alpha)**beta) / (2 * gamma(1/beta))) 


main = do
    let x = pdf 0 1 2 0.5
    print x
    let y = cdf 0 1 2 0.5
    print y

Answer 1

Your code looks fine to me. If you wish, you could use Greek letters. This makes the formula easier to read, but if you expect to modify it often, it may be too much trouble to enter the Greek letters. You might find it helpful to split up long formulas, as I've done for pdf. If you can think of more meaningful names than foo and bar, this might be a good idea. However, if this is a well-known formula in your field, splitting it up might actually make it less recognisable. It's a judgement call.

If you wrote this in literate Haskell, you could include a nicely-formatted version of the formula using LaTeX. That might be useful if you're writing code with a lot of formulas.

import Math.Gamma

γ :: Double -> Double
γ = gamma

pdf :: Double -> Double -> Double -> Double -> Double
pdf μ α β x = foo ** bar ** β
  where foo = ( β / (2 * α * γ  ( 1/β) ) )
        bar = exp ( -1* ( abs(x - μ )/α ))

cdf :: Double -> Double -> Double -> Double -> Double
cdf μ α β x = 0.5 + signum(x - μ) * ( lowerGamma  (1/β) ((abs(x-μ) / α)**β) / (2 * γ(1/β))) 


main = do
    let x = pdf 0 1 2 0.5
    print x
    let y = cdf 0 1 2 0.5
    print y