Data.Monoid.Statistics.Numeric

Contents

Synopsis

Mean and variance

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 aSource

Fix type of monoid

data Mean Source

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 Source

Fix type of monoid

data Variance Source

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 Source

Fix type of monoid

Ad-hoc accessors

Monoids Count, Mean and Variance form some kind of tower. Every successive monoid can calculate every statistics previous monoids can. So to avoid replicating accessors for each statistics a set of ad-hoc type classes was added.

This approach have deficiency. It becomes to infer type of monoidal accumulator from accessor function so following expression will be rejected:

 calcCount $ evalStatistics xs

Indeed type of accumulator is:

 forall a . (StatMonoid a, CalcMean a) => a

Therefore it must be fixed by adding explicit type annotation. For example:

 calcMean (evalStatistics xs :: Mean)

class CalcCount m whereSource

Statistics which could count number of elements in the sample

Methods

calcCount :: m -> Int Source

Number of elements in sample

Instances

CalcCount Variance
CalcCount Mean
CalcCount (Count Int)

class CalcMean m whereSource

Statistics which could estimate mean of sample

Methods

calcMean :: m -> Double Source

Calculate esimate of mean of a sample

Instances

CalcMean Variance
CalcMean Mean

class CalcVariance m whereSource

Statistics which could estimate variance of sample

Methods

calcVariance :: m -> Double Source

Calculate biased estimate of variance

calcVarianceUnbiased :: m -> Double Source

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

Instances

CalcVariance Variance

calcStddev :: CalcVariance m => m -> Double Source

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

calcStddevUnbiased :: CalcVariance m => m -> Double Source

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

Maximum and minimum

newtype Max Source

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 Source

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