module Math.Statistics where
import List
mean :: (Floating a) => [a] -> a
mean xs = sum xs / (fromIntegral . length) xs
hmean :: (Floating a) => [a] -> a
hmean xs = fromIntegral (length xs) / (sum $ map (1/) xs)
gmean :: (Floating a) => [a] -> a
gmean xs = (foldr1 (*) xs)**(1 / fromIntegral (length xs))
median :: (Floating a, Ord a) => [a] -> a
median x | odd n = head $ drop (n `div` 2) x'
| even n = mean $ take 2 $ drop i x'
where i = (length x' `div` 2) 1
x' = sort x
n = length x
modes :: (Ord a) => [a] -> [(Int, a)]
modes xs = sortOn (negate.fst) $ map (\x->(length x, head x)) $ (group.sort) xs
where
sortOn :: Ord b => (a -> b) -> [a] -> [a]
sortOn f = sortBy (\x y -> compare (f x) (f y))
range :: (Num a, Ord a) => [a] -> a
range xs = maximum xs minimum xs
avgdev :: (Floating a) => [a] -> a
avgdev xs = mean $ map (\x -> abs(x m)) xs
where
m = mean xs
stddev :: (Floating a) => [a] -> a
stddev xs = sqrt $ var xs
pvar :: (Floating a) => [a] -> a
pvar xs = mean $ map (\x -> (x m)^2) xs
where
m = mean xs
var :: (Floating a) => [a] -> a
var xs = (sum $ map (\x -> (x m)^2) xs) / (fromIntegral (length xs)1)
where
m = mean xs
iqr xs = take (length xs 2*q) $ drop q xs
where
q = ((length xs) + 1) `div` 4
kurtosis :: (Floating b) => [b] -> b
kurtosis xs = sum (map (\x -> ((x m) / (stddev xs))^4) xs) / n 3
where
m = mean xs
n = fromIntegral $ length $ xs
skew :: (Floating a) => [a] -> a
skew xs = mean $ (map (\x -> ((x (mean xs)) / (stddev xs))^3) xs)
cov :: (Floating a) => [a] -> [a] -> a
cov xs ys = sum (zipWith (*) (map f1 xs) (map f2 ys)) / (n 1)
where
n = fromIntegral $ length $ xs
m1 = mean xs
m2 = mean ys
f1 = \x -> (x m1)
f2 = \x -> (x m2)
covm :: (Floating a) => [[a]] -> [[a]]
covm xs = split' (length xs) cs
where
cs = [ cov a b | a <- xs, b <- xs]
split' n = unfoldr (\y -> if null y then Nothing else Just $ splitAt n y)
corr :: (Floating a) => [a] -> [a] -> a
corr x y = cov x y / (stddev x * stddev y)