mir.stat.descriptive.univariate

This module contains algorithms for univariate descriptive statistics.

Note that used specialized summing algorithms execute more primitive operations than vanilla summation. Therefore, if in certain cases maximum speed is required at expense of precision, one can use $(TT Summation.fast) .


Category	Symbols
Location	gmean hmean mean median
Deviation	dispersion entropy interquartileRange medianAbsoluteDeviation quantile standardDeviation variance
Higher Moments, etc.	kurtosis skewness
Other Moment Functions	centralMoment coefficientOfVariation moment rawMoment standardizedMoment
Accumulators	EntropyAccumulator GMeanAccumulator KurtosisAccumulator MeanAccumulator MomentAccumulator SkewnessAccumulator VarianceAccumulator
Algorithms	KurtosisAlgo MomentAlgo QuantileAlgo SkewnessAlgo StandardizedMomentAlgo VarianceAlgo
Types	entropyType gmeanType hmeanType meanType quantileType statType stdevType

Members

Enums

KurtosisAlgo enum KurtosisAlgo: Kurtosis algorithms.
MomentAlgo enum MomentAlgo
QuantileAlgo enum QuantileAlgo: Algorithms used to calculate the quantile of an input x at probability p.
SkewnessAlgo enum SkewnessAlgo: Skewness algorithms.
StandardizedMomentAlgo enum StandardizedMomentAlgo
Summation (from mir.math.sum) enum Summation via public import mir.math.sum : Summation;
VarianceAlgo enum VarianceAlgo: Variance algorithms.

Functions

gmean gmeanType!F gmean(Range r)
gmeanType!Range gmean(Range r): Computes the geometric average of the input.
gmean gmeanType!F gmean(F[] ar)
median meanType!(T[]) median(T[] ar)
median auto median(T sliceLike)
medianAbsoluteDeviation meanType!(Slice!(Iterator, N, kind)) medianAbsoluteDeviation(Slice!(Iterator, N, kind) slice)
meanType!(T[]) medianAbsoluteDeviation(T[] ar)
auto medianAbsoluteDeviation(SliceLike x): Calculates the median absolute deviation about the median of the input.

Structs

EntropyAccumulator struct EntropyAccumulator(T, Summation summation)
GMeanAccumulator struct GMeanAccumulator(T): Output range for gmean.
KurtosisAccumulator struct KurtosisAccumulator(T, KurtosisAlgo kurtosisAlgo, Summation summation)
KurtosisAccumulator struct KurtosisAccumulator(T, KurtosisAlgo kurtosisAlgo, Summation summation)
KurtosisAccumulator struct KurtosisAccumulator(T, KurtosisAlgo kurtosisAlgo, Summation summation)
KurtosisAccumulator struct KurtosisAccumulator(T, KurtosisAlgo kurtosisAlgo, Summation summation)
KurtosisAccumulator struct KurtosisAccumulator(T, KurtosisAlgo kurtosisAlgo, Summation summation)
KurtosisAccumulator struct KurtosisAccumulator(T, KurtosisAlgo kurtosisAlgo, Summation summation)
MapSummator struct MapSummator(alias fun, T, Summation summation): Output range that applies function fun to each input before summing
MeanAccumulator struct MeanAccumulator(T, Summation summation): Output range for mean.
MomentAccumulator struct MomentAccumulator(T, size_t N, Summation summation)
SkewnessAccumulator struct SkewnessAccumulator(T, SkewnessAlgo skewnessAlgo, Summation summation)
SkewnessAccumulator struct SkewnessAccumulator(T, SkewnessAlgo skewnessAlgo, Summation summation)
SkewnessAccumulator struct SkewnessAccumulator(T, SkewnessAlgo skewnessAlgo, Summation summation)
SkewnessAccumulator struct SkewnessAccumulator(T, SkewnessAlgo skewnessAlgo, Summation summation)
SkewnessAccumulator struct SkewnessAccumulator(T, SkewnessAlgo skewnessAlgo, Summation summation)
SkewnessAccumulator struct SkewnessAccumulator(T, SkewnessAlgo skewnessAlgo, Summation summation)
VarianceAccumulator struct VarianceAccumulator(T, VarianceAlgo varianceAlgo, Summation summation)
VarianceAccumulator struct VarianceAccumulator(T, VarianceAlgo varianceAlgo, Summation summation)
VarianceAccumulator struct VarianceAccumulator(T, VarianceAlgo varianceAlgo, Summation summation)
VarianceAccumulator struct VarianceAccumulator(T, VarianceAlgo varianceAlgo, Summation summation)
VarianceAccumulator struct VarianceAccumulator(T, VarianceAlgo varianceAlgo, Summation summation)

Templates

centralMoment template centralMoment(F, size_t N, Summation summation = Summation.appropriate)
template centralMoment(size_t N, Summation summation = Summation.appropriate)
template centralMoment(F, size_t N, string summation)
template centralMoment(size_t N, string summation): Calculates the n-th central moment of the input.
coefficientOfVariation template coefficientOfVariation(F, VarianceAlgo varianceAlgo = VarianceAlgo.hybrid, Summation summation = Summation.appropriate)
template coefficientOfVariation(VarianceAlgo varianceAlgo = VarianceAlgo.hybrid, Summation summation = Summation.appropriate): Calculates the coefficient of variation of the input.
coefficientOfVariation template coefficientOfVariation(F, string varianceAlgo, string summation = "appropriate")
template coefficientOfVariation(string varianceAlgo, string summation = "appropriate")
dispersion template dispersion(alias centralTendency = mean, alias transform = "a * a", alias summarize = mean): Calculates the dispersion of the input.
entropy template entropy(F, Summation summation = Summation.appropriate): Computes the entropy of the input. By default, if F is not a floating point type, then the result will have a double type if F is implicitly convertible to a floating point type.
entropy template entropy(Summation summation = Summation.appropriate)
template entropy(F, string summation)
template entropy(string summation)
entropyType template entropyType(T): If T is a floating point type, this is an alias to the unqualified type. If T is not a floating point type, this will alias a double type if T is summable and implicitly convertible to a floating point type.
gmeanType template gmeanType(T)
hmean template hmean(F, Summation summation = Summation.appropriate)
template hmean(Summation summation = Summation.appropriate)
template hmean(F, string summation)
template hmean(string summation): Computes the harmonic mean of the input.
hmeanType template hmeanType(T)
interquartileRange template interquartileRange(F, QuantileAlgo quantileAlgo = QuantileAlgo.type7, bool allowModifySlice = false)
template interquartileRange(QuantileAlgo quantileAlgo = QuantileAlgo.type7, bool allowModifySlice = false)
template interquartileRange(F, string quantileAlgo, bool allowModifySlice = false)
template interquartileRange(string quantileAlgo, bool allowModifySlice = false): Computes the interquartile range of the input.
kurtosis template kurtosis(F, KurtosisAlgo kurtosisAlgo = KurtosisAlgo.hybrid, Summation summation = Summation.appropriate)
template kurtosis(KurtosisAlgo kurtosisAlgo = KurtosisAlgo.hybrid, Summation summation = Summation.appropriate)
template kurtosis(F, string kurtosisAlgo, string summation = "appropriate")
template kurtosis(string kurtosisAlgo, string summation = "appropriate"): Calculates the kurtosis of the input
mean template mean(F, Summation summation = Summation.appropriate)
template mean(Summation summation = Summation.appropriate)
template mean(F, string summation)
template mean(string summation): Computes the mean of the input.
meanType template meanType(T)
median template median(F, bool allowModify = false)
template median(bool allowModify = false): Computes the median of slice.
medianAbsoluteDeviation template medianAbsoluteDeviation(F): Calculates the median absolute deviation about the median of the input.
moment template moment(F, size_t N, MomentAlgo momentAlgo, Summation summation = Summation.appropriate)
template moment(size_t N, MomentAlgo momentAlgo, Summation summation = Summation.appropriate)
template moment(F, size_t N, string momentAlgo, string summation = "appropriate")
template moment(size_t N, string momentAlgo, string summation = "appropriate"): Calculates the n-th moment of the input.
quantile template quantile(F, QuantileAlgo quantileAlgo = QuantileAlgo.type7, bool allowModifySlice = false, bool allowModifyProbability = false): Computes the quantile(s) of the input, given one or more probabilities p.
quantile template quantile(QuantileAlgo quantileAlgo = QuantileAlgo.type7, bool allowModifySlice = false, bool allowModifyProbability = false)
template quantile(F, string quantileAlgo, bool allowModifySlice = false, bool allowModifyProbability = false)
template quantile(string quantileAlgo, bool allowModifySlice = false, bool allowModifyProbability = false)
quantileType template quantileType(T, QuantileAlgo quantileAlgo): For all QuantileAlgo except QuantileAlgo.type1 and QuantileAlgo.type3, this is an alias to the $(MATHREF stat, meanType) of T
rawMoment template rawMoment(F, size_t N, Summation summation = Summation.appropriate)
template rawMoment(size_t N, Summation summation = Summation.appropriate)
template rawMoment(F, size_t N, string summation)
template rawMoment(size_t N, string summation): Calculates the n-th raw moment of the input.
skewness template skewness(F, SkewnessAlgo skewnessAlgo = SkewnessAlgo.hybrid, Summation summation = Summation.appropriate)
template skewness(SkewnessAlgo skewnessAlgo = SkewnessAlgo.hybrid, Summation summation = Summation.appropriate)
template skewness(F, string skewnessAlgo, string summation = "appropriate")
template skewness(string skewnessAlgo, string summation = "appropriate"): Calculates the skewness of the input
standardDeviation template standardDeviation(F, VarianceAlgo varianceAlgo = VarianceAlgo.hybrid, Summation summation = Summation.appropriate)
template standardDeviation(VarianceAlgo varianceAlgo = VarianceAlgo.hybrid, Summation summation = Summation.appropriate)
template standardDeviation(F, string varianceAlgo, string summation = "appropriate")
template standardDeviation(string varianceAlgo, string summation = "appropriate"): Calculates the standard deviation of the input
standardizedMoment template standardizedMoment(F, size_t N, StandardizedMomentAlgo standardizedMomentAlgo = StandardizedMomentAlgo.scaled, VarianceAlgo varianceAlgo = VarianceAlgo.twoPass, Summation summation = Summation.appropriate)
template standardizedMoment(size_t N, StandardizedMomentAlgo standardizedMomentAlgo = StandardizedMomentAlgo.scaled, VarianceAlgo varianceAlgo = VarianceAlgo.twoPass, Summation summation = Summation.appropriate)
template standardizedMoment(F, size_t N, string standardizedMomentAlgo, string varianceAlgo = "twoPass", string summation = "appropriate")
template standardizedMoment(size_t N, string standardizedMomentAlgo, string varianceAlgo = "twoPass", string summation = "appropriate"): Calculates the n-th standardized moment of the input.
statType template statType(T, bool checkComplex = true)
stdevType template stdevType(T)
variance template variance(F, VarianceAlgo varianceAlgo = VarianceAlgo.hybrid, Summation summation = Summation.appropriate)
template variance(VarianceAlgo varianceAlgo = VarianceAlgo.hybrid, Summation summation = Summation.appropriate)
template variance(F, string varianceAlgo, string summation = "appropriate")
template variance(string varianceAlgo, string summation = "appropriate"): Calculates the variance of the input

The OpenD Programming Language

mir.stat.descriptive.univariate

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