Numeric.Statistics

Useful statistical functions

Documentation

type Sample a = Vector a

type Samples a = Array Int (Vector a)

covarianceMatrix

Arguments

:: Samples Double

the dimensions of data (each vector being one dimension)

-> Matrix Double

the symmetric covariance matrix

the covariance matrix

correlationCoefficientMatrix :: Samples Double -> Matrix Double

the correlation coefficient: (cov x y) / (std x) (std y)

meanList :: (Container Vector a, Num (Vector a), Fractional a) => [Sample a] -> Sample a

the mean of a list of vectors

meanArray :: (Container Vector a, Num (Vector a), Fractional a) => Samples a -> Sample a

the mean of an array of vectors

meanMatrix :: (Container Vector a, Num (Vector a), Fractional a) => Matrix a -> Sample a

the mean of a matrix with data series in rows

varianceList :: (Container Vector a, Floating (Vector a), Num a, Fractional a) => [Sample a] -> Sample a

the variance of a list of vectors

varianceArray :: (Container Vector a, Floating (Vector a), Fractional a) => Samples a -> Sample a

the variance of an array of vectors

varianceMatrix :: (Container Vector a, Floating (Vector a), Fractional a) => Matrix a -> Sample a

the variance of a matrix with data series in rows

centre :: Vector Double -> Vector Double

centre the data to 0: (x - (mean x))

cloglog :: Floating a => a -> a

complementary log-log function cloglog :: Vector Double -> Vector Double

corcoeff :: Vector Double -> Vector Double -> Double

corcoeff = covariance x / (std dev x * std dev y)

cut

Arguments

:: Vector Double

-> Vector Double

intervals

-> Vector Int

data indexed by bin

cut numerical data into intervals, data must fall inside the bounds

ranks :: (Fractional b, Storable b) => Vector Double -> Vector b

return the rank of each element of the vector multiple identical entries result in the average rank of those entries ranks :: Vector Double -> Vector Double

kendall :: Vector Double -> Vector Double -> Matrix Double

kendall's rank correlation τ

logit :: (Floating b, Storable b) => Vector b -> Vector b

(logit p) = log(p/(1-p)) logit :: Vector Double -> Vector Double

mahalanobis

Arguments

:: Samples Double

the data set

-> Maybe (Sample Double)

(Just sample) to be measured or use mean when Nothing

-> Double

D^2

the Mahalanobis D-square distance between samples columns are components and rows are observations (uses pseudoinverse)

mode :: Vector Double -> [(Double, Integer)]

a list of element frequencies

moment

Arguments

:: Integral a

=> a

moment

-> Bool

calculate central moment

-> Bool

calculate absolute moment

-> Vector Double

data

-> Double

the p'th moment of a vector

ols

Arguments

:: (Num (Vector t), Field t)

=> Matrix t

X

-> Matrix t

Y

-> (Matrix t, Matrix t, Matrix t)

(OLS estimator for B, OLS estimator for s, OLS residuals)

ordinary least squares estimation for the multivariate model Y = X B + e rows are observations, columns are elements mean e = 0, cov e = kronecker s I

percentile

Arguments

:: Double

percentile (0 - 100)

-> Vector Double

data

-> Double

result

compute quantiles in percent

range :: (Container c e, Num e) => c e -> e

the difference between the maximum and minimum of the input

run_count

Arguments

:: (Num a, Num t, Ord b, Ord a, Container Vector b)

=> a

longest run to count

-> Vector b

data

-> [(a, t)]

(run length,count)

count the number of runs greater than or equal to n in the data

spearman :: Vector Double -> Vector Double -> Double

Spearman's rank correlation coefficient

studentize :: Vector Double -> Vector Double

centre and normalise a vector