This page provides stand-alone Haskell code for computing the quantile function, or inverse CDF, for the standard normal probability distribution. The accuracy is modest, but the code is brief and completely self-contained; you can simply copy and paste it into your project.

If you’re willing to take an external dependence, you can get higher accuracy from math-functions and use the formulas here to implement the inverse of the normal CDF in terms of that module’s function `invErf`

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The code below is based on Formula 26.2.23 from Abramowitz and Stegun.

The code is simply as follows:

rational_approx :: Double -> Double rational_approx t = t - ((0.010328*t + 0.802853)*t + 2.515517) / (((0.001308*t + 0.189269)*t + 1.432788)*t + 1.0); phi_inverse :: Double -> Double phi_inverse p = if p < 0.5 then - rational_approx( sqrt (-2.0*log(p)) ) else rational_approx( sqrt (-2.0*log(1.0 - p)) )

The test code is longer than the code itself.

test_phi_inverse :: Bool test_phi_inverse = maximum error < epsilon where error = [ abs(phi_inverse x - y) | (x, y) <- zip xs ys ] xs = [0.0000001, 0.00001, 0.001, 0.05, 0.15, 0.25, 0.35, 0.45, 0.55, 0.65, 0.75, 0.85, 0.95, 0.999, 0.99999, 0.9999999] ys = [-5.199337582187471, -4.264890793922602, -3.090232306167813, -1.6448536269514729, -1.0364333894937896, -0.6744897501960817, -0.38532046640756773, -0.12566134685507402, 0.12566134685507402, 0.38532046640756773, 0.6744897501960817, 1.0364333894937896, 1.6448536269514729, 3.090232306167813, 4.264890793922602, 5.199337582187471] epsilon = 4.5e-4 -- Accuracy advertised in A&S 26.2.23