Data.Monoid.Statistics.Numeric

Mean and variance

newtype Count a

Simplest statistics. Number of elements in the sample

Constructors

Count

Fields

calcCountI :: a

Instances

Typeable1 Count

Eq a => Eq (Count a)

Ord a => Ord (Count a)

Show a => Show (Count a)

Integral a => Monoid (Count a)

CalcCount (Count Int)

Integral a => StatMonoid (Count a) b

asCount :: Count a -> Count a

Fix type of monoid

data Mean

Mean of sample. Samples of Double,Float and bui;t-in integral types are supported

Numeric stability of mappend is not proven.

Constructors

Mean !Int !Double

Instances

Eq Mean

Show Mean

Typeable Mean

Monoid Mean

CalcMean Mean

CalcCount Mean

Real a => StatMonoid Mean a

asMean :: Mean -> Mean

Fix type of monoid

data Variance

Intermediate quantities to calculate the standard deviation.

Constructors

Variance !Int !Double !Double

Instances

Eq Variance

Show Variance

Typeable Variance

Monoid Variance

Using parallel algorithm from:

Chan, Tony F.; Golub, Gene H.; LeVeque, Randall J. (1979), Updating Formulae and a Pairwise Algorithm for Computing Sample Variances., Technical Report STAN-CS-79-773, Department of Computer Science, Stanford University. Page 4.

ftp://reports.stanford.edu/pub/cstr/reports/cs/tr/79/773/CS-TR-79-773.pdf

CalcVariance Variance

CalcMean Variance

CalcCount Variance

Real a => StatMonoid Variance a

asVariance :: Variance -> Variance

Fix type of monoid

Ad-hoc accessors

class CalcCount m where

Methods

calcCount :: m -> Int

Number of elements in sample

Instances

CalcCount Variance

CalcCount Mean

CalcCount (Count Int)

class CalcMean m where

Methods

calcMean :: m -> Double

Calculate esimate of mean of a sample

Instances

CalcMean Variance

CalcMean Mean

class CalcVariance m where

Methods

calcVariance :: m -> Double

Calculate biased estimate of variance

calcVarianceUnbiased :: m -> Double

Calculate unbiased estimate of the variance, where the denominator is $n-1$.

Instances

CalcVariance Variance

calcStddev :: CalcVariance m => m -> Double

Calculate sample standard deviation (biased estimator, $s$, where the denominator is $n-1$).

calcStddevUnbiased :: CalcVariance m => m -> Double

Calculate standard deviation of the sample (unbiased estimator, $sigma$, where the denominator is $n$).

Maximum and minimum

newtype Max

Calculate maximum of sample. For empty sample returns NaN. Any NaN encountedred will be ignored.

Constructors

Max

Fields

calcMax :: Double

Instances

Eq Max

Ord Max

Show Max

Typeable Max

Monoid Max

StatMonoid Max Double

newtype Min

Calculate minimum of sample. For empty sample returns NaN. Any NaN encountedred will be ignored.

Constructors

Min

Fields

calcMin :: Double

Instances

Eq Min

Ord Min

Show Min

Typeable Min

Monoid Min

StatMonoid Min Double