------------------------------------------------------------------------ -- | -- Module : Math.Statistics -- Copyright : (c) Johan Tibell 2008 -- License : BSD3-style (see LICENSE) -- -- Maintainer : me@willsewell.com -- Stability : experimental -- Portability : portable -- -- Common statistical functions. -- ------------------------------------------------------------------------ module Math.Statistics ( mean , median , stddev , variance ) where import Data.List (sort) -- | Numerically stable mean. mean :: Floating a => [a] -> a mean = go 0 0 where go :: Floating a => a -> Int -> [a] -> a go m _ [] = m go m n (x:xs) = go (m + (x - m) / fromIntegral (n + 1)) (n + 1) xs -- | Median. median :: (Floating a, Ord a) => [a] -> a median xs | odd n = head \$ drop (n `div` 2) xs' | otherwise = mean \$ take 2 \$ drop i xs' where i = (length xs' `div` 2) - 1 xs' = sort xs n = length xs -- | Standard deviation. stddev :: Floating a => [a] -> a stddev xs = sqrt \$ variance xs -- | Numerically stable sample variance. variance :: Floating a => [a] -> a variance xs = go 0 0 0 xs / fromIntegral (length xs - 1) where go :: Floating a => a -> Int -> a -> [a] -> a go _ _ s [] = s go m n s (x:xs') = go nm (n + 1) (s + delta * (x - nm)) xs' where delta = x - m nm = m + delta / fromIntegral (n + 1)