{- Module : HNumeric.Stats Description : Haskell Statistics Library with HNum.Vector CopyRight : (c) Tae Geun Kim, 2018 License : BSD3 Maintainer : edeftg@gmail.com Stability : Experimental -} module HNum.Stats where import HNum.Vector import HNum.CSV -- | To contain coefficients of linear regression. type Coeff a = (a, a) -------------------------------------------------------- -- Basic Probability -------------------------------------------------------- -- | Factorial fac :: Integral a => a -> a fac 0 = 1 fac 1 = 1 fac n = product [1 .. n] -- | Factorial with start n,end s facStop :: Integral a => a -> a -> a facStop n s = product [s .. n] -- | Permutation p :: Integral a => a -> a -> a n `p` r = facStop n (n - r + 1) -- | Combination using permutation c :: Integral a => a -> a -> a n `c` r = (n `p` r) `div` fac r -------------------------------------------------------- -- Basic Statistics -------------------------------------------------------- -- | Basic Statistics Class for Vector class VecOps v => Statistical v where -- | Sample Mean mean :: Fractional a => v a -> a -- | Single Valued covariance cov' :: Floating a => v a -> v a -> a -- | Covariance Matrix cov :: Floating a => v a -> v a -> Matrix a -- | Sample Variance var :: Floating a => v a -> a -- | Sample Standard deviation std :: Floating a => v a -> a -- | Standard Error se :: Floating a => v a -> a -- | Correlation Coefficient cor :: Floating a => v a -> v a -> a -- | Median med :: (Ord a, Floating a) => v a -> a -- | Mode mode :: Eq a => v a -> a -- | Coefficient of Variation cv :: Floating a => v a -> a -- | Moment moment :: Floating a => a -> v a-> a -- | Skewness skew :: Floating a => v a -> a -- | Skewness 2 skew' :: Floating a => v a -> a -- | kurtosis kurt :: Floating a => v a -> a instance Statistical Vector where -- mean mean x = sum x / fromIntegral (length x) -- cov' cov' x y | length x <= 1 || length y <= 1 = error "Samples are not enough" | length x /= length y = error "Length is not same" | otherwise = ((x .- mean x) .*. (y .- mean y)) / fromIntegral (length x - 1) -- cov cov x y = matrix [[var x, cov' x y], [cov' y x, var y]] -- var var v = cov' v v -- std std = sqrt . var -- se se x = std x / sqrt (fromIntegral (length x)) -- cor cor x y = cov' x y / (std x * std y) -- med med x | even l = ((qs !! (l'-1)) + (qs !! l')) / 2 | otherwise = qs !! l' where l = length x l' = l `div` 2 qs = (toList . qsort) x -- mode mode x = v !! n where v = toList x cx = map (`count` v) v m = maximum cx n = head \$ dropWhile (\p -> cx !! p /= m) [0..] -- cv cv x = std x / mean x -- moment moment n x = sum ((x .- mean x) .^ n) -- skew skew x = (1 / fromIntegral l) * moment 3 x / std x ^ 3 where l = length x skew' x = (fromIntegral l^2 / fromIntegral ((l-1) * (l-2))) * skew x where l = length x -- kurt kurt x = moment 4 x / (fromIntegral l * std x ** 4) - 3 where l = length x -------------------------------------------------------- -- For IO -------------------------------------------------------- summary :: (Show a, Floating a) => DataFrame a -> IO () summary df = do putStrLn \$ "Mean: " ++ show hm putStrLn \$ "Var: " ++ show hv putStrLn \$ "Std: " ++ show hs where h = header df m = matForm \$ dat df ms = map (mean . vector) m vs = map (var . vector) m ss = map (std . vector) m hm = zip h ms hv = zip h vs hs = zip h ss describe :: (Show a, Floating a, Ord a) => Vector a -> IO () describe v = do putStrLn \$ "n: " ++ show (length v) putStrLn \$ "mean: " ++ show (mean v) putStrLn \$ "std: " ++ show (std v) putStrLn \$ "med: " ++ show (med v) putStrLn \$ "mode: " ++ show (mode v) putStrLn \$ "min: " ++ show (minimum v) putStrLn \$ "max: " ++ show (maximum v) putStrLn \$ "skew: " ++ show (skew v) putStrLn \$ "kurt: " ++ show (kurt v) putStrLn \$ "SE: " ++ show (se v) -------------------------------------------------------- -- Linear Regression -------------------------------------------------------- -- | Least Square Method - (Intercept, Slope) lm :: Floating a => Vector a -> Vector a -> Coeff a lm x y = (my - b1 * mx, b1) where mx = mean x my = mean y b1 = (x .- mx) .*. (y .- my) / ((x .- mx) .*. (x .- mx)) -- | Line Fitting with (Intercept, Slope) & Range of x lineFit :: Floating a => Coeff a -> Vector a -> Vector a lineFit (n, m) x = x .* m .+ n -- | Residual Sum of Squares rss :: Floating a => Vector a -> Vector a -> a rss x y = sum ((y - lineFit (lm x y) x) .^ 2) -- | Relative Standard Error rse :: Floating a => Vector a -> Vector a -> a rse x y = sqrt (1 / fromIntegral (length x - 2) * rss x y) -------------------------------------------------------- -- Technical Analysis -------------------------------------------------------- -- | Simple Moving Average sma :: Fractional a => Int -> Vector a -> Vector a sma p v = vec \$ take (p - 1) v' ++ sma' p v' where v' = toList v sma' :: Fractional a => Int -> [a] -> [a] sma' p x | length x < p = [] | otherwise = let m = sum (take p x) / fromIntegral p in m : sma' p (tail x) -------------------------------------------------------- -- Backend Functions -------------------------------------------------------- -- | Count Elements count :: Eq a => a -> [a] -> Int count p v = length (filter (== p) v)