EPS formulas

-- EPS formulas for mean and variance calculations
mean :: [Float] -> Float
mean [] = 0
mean x = sum x / fromIntegral (length x)

s :: [Float] -> Float
s [] = 0
s x = sqrt ((sum (map (\xs -> (xs - (mean x)) ** 2) x)) / (fromIntegral ((length x) - 1)))

-- recursive versions

s_recursive :: [Float] -> Float
s_recursive [] = 0
s_recursive x = sqrt ((aux x (mean x)) / (fromIntegral ((length x) - 1)))
    where
        aux [] _ = 0
        aux (x : xs) y = ((x - y) ** 2) + aux xs y

mean_recursive :: [Float] -> Float
mean_recursive [] = 0
mean_recursive x = aux x / fromIntegral (length x)
    where
        aux [] = 0
        aux (x : xs) = x + aux xs