kumulant/com.eignex.kumulant.core/HasShapeMoments

HasShapeMoments

interface HasShapeMoments : HasSampleVariance(source)

Result trait for accumulators that expose third and fourth central moments plus skewness and kurtosis. Extends HasSampleVariance; every shape moment result is also a variance result.

Implemented by com.eignex.kumulant.stat.summary.MomentsResult. Use it when the shape of the distribution matters; heavy tails (kurtosis), asymmetry (skewness), departures from normality in general.

Biased (skewness, kurtosis) and unbiased (unbiasedSkewness, unbiasedKurtosis) variants are both exposed. Pick biased for the moment estimate itself, unbiased when feeding into a small-sample inference test.

Inheritors

MomentsResult

Properties

kurtosis

open val kurtosis: Double

Biased excess kurtosis: (m4 / w) / variance^2 - 3. Heavy tails are positive; the - 3 normalises so that a Gaussian has excess kurtosis 0.

open val m2: Double

Raw 2nd central moment: Sum (x - mean)^2 * weight. Identical to sst.

abstract val m3: Double

Raw 3rd central moment: Sum (x - mean)^3 * weight.

abstract val m4: Double

Raw 4th central moment: Sum (x - mean)^4 * weight.

sampleStdDev

open val sampleStdDev: Double

Unbiased sample standard deviation: sqrt([sampleVariance]).

sampleVariance

open val sampleVariance: Double

Unbiased sample variance: [sst] / ([totalWeights] - 1). Zero when totalWeights <= 1.

skewness

open val skewness: Double

Biased skewness: (m3 / w) / variance^1.5. Standardised third moment; 0 for symmetric distributions, positive for right tails, negative for left tails.

sst

open val sst: Double

Sum of squared deviations from the running mean: Sum (x - mean)^2 * weight.

stdDev

open val stdDev: Double

Population standard deviation: sqrt([variance]).

totalWeights

abstract val totalWeights: Double

Cumulative weight of observations folded into this result.

unbiasedKurtosis

open val unbiasedKurtosis: Double

Sample-size-adjusted (unbiased) excess kurtosis. Zero when totalWeights <= 3.

unbiasedSkewness

open val unbiasedSkewness: Double

Sample-size-adjusted (unbiased) skewness. Zero when totalWeights <= 2.

variance

open val variance: Double

Population variance: [sst] / [totalWeights]. Zero on an empty stream.

kurtosis

open val kurtosis: Double(source)

Biased excess kurtosis: (m4 / w) / variance^2 - 3. Heavy tails are positive; the - 3 normalises so that a Gaussian has excess kurtosis 0.

m2

open val m2: Double(source)

Raw 2nd central moment: Sum (x - mean)^2 * weight. Identical to sst.

m3

abstract val m3: Double(source)

Raw 3rd central moment: Sum (x - mean)^3 * weight.

m4

abstract val m4: Double(source)