inhomoSum :: RealFloat a => [a] -> a
inhomoSum xs
  =  sum [ ((s1 n)**2 + (s2 n)**2) / n**2
         | i <- [1..huge], n <- [fromIntegral i] ]
  where
    s1 n  =  sum [ cos (2 * pi * n * x) | x <- xs ]
    s2 n  =  sum [ sin (2 * pi * n * x) | x <- xs ]
    huge  =  1000

inhomoSignificance :: RealFloat a => [a] -> a
inhomoSignificance xs
  | xs == []   =  error "inhomoSignificance undefined for empty list"
  | otherwise  =  prob (inhomoSum xs / count)
  where
    count   =  fromIntegral (length xs)
    prob x  =  limit (
                 sum [ (if i < huge then 2 else 1) *
                       (-1)**(n-1) * exp (-n**2 * x)
                     | i <- [1..huge], n <- [fromIntegral i] ]
               )
    limit   = (min 1 . max 0)
    huge    =  1000

inhomogeneity :: RealFloat a => [a] -> a
inhomogeneity xs
  | xs == []        =  error "inhomogenity undefined for empty list"
  | length xs == 1  =  error "inhomogenity undefined for single value"
  | otherwise       =  sqrt ( limit (
                         (inhomoSum xs * 6 / pi**2 - 1) /
                         (count**2 - 1)
                       ) )
  where
    count  =  fromIntegral (length xs)
    limit  =  max 0