Coefficient of Variation and Scale Comparability

Install and import#

npm install fintech-algorithms

import { coefficientOfVariationAndScaleComparability } from "fintech-algorithms/foundations/dispersion-shape-and-robust-statistics/coefficient-of-variation-and-scale-comparability";

Signature#

coefficientOfVariationAndScaleComparability(input)

Divides the sample standard deviation by the absolute value of the mean, turning spread into a unit-free figure that can be compared across series measured on different scales.

Parameters#

Returns#

{ coefficientOfVariation: number; scaleFree: boolean }

coefficientOfVariation is the sample standard deviation over the absolute mean, and scaleFree is always true, marking the figure as carrying no units.

Errors#

• When input is null, an array, or not an object — throws TypeError
• When values is missing, is not an array, or is empty — throws RangeError
• When any entry of values does not coerce to a finite number — throws RangeError
• When values holds fewer than two observations, so the sample divisor n - 1 would be zero — throws RangeError
• When the arithmetic mean of values is exactly zero, leaving the ratio undefined — throws RangeError

Complexity: time O(n log n), space O(n).

Worked example#

verified This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

Input#

{
  "values": [1, 2, 2, 4, 9]
}

Call#

coefficientOfVariationAndScaleComparability(input)

Returns#

object with 2 fields: coefficientOfVariation, scaleFree

{
  "coefficientOfVariation": 0.8914892519934007,
  "scaleFree": true
}

Diagrams#

How it works#

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References#

• Measures of Scale — NIST/SEMATECH e-Handbook
• Skewness and Kurtosis — NIST/SEMATECH e-Handbook
• Historical-example decision

The rest of the Dispersion, Shape, and Robust Statistics family#

• Deviation, Absolute Deviation, and Squared DeviationCentres a numeric series on its arithmetic mean and returns the three per-observation distance forms built from that centring: …
• Range and Interquartile RangeMeasures spread two ways on the same series: the full distance from smallest to largest, and the distance covering the middle h…
• Mean Absolute DeviationAverages the absolute distances of the observations from their arithmetic mean, giving a spread figure in the same units as the…
• Median Absolute DeviationTakes the median of the absolute distances from the series median, and rescales it by 1.4826 so it lines up with a standard dev…
• Population and Sample VarianceAverages the squared deviations from the mean twice over the same series: once dividing by the observation count, once by that …
• Population and Sample Standard DeviationTakes the square root of both the population and the sample variance of one series, returning spread in the same units as the o…
• Z-Score, Robust Z-Score, and StandardizationStandardises every observation twice: once against the mean and sample standard deviation, and once against the median and medi…
• Skewness and Tail AsymmetryDivides the third central moment by the second raised to the power 1.5, giving the moment coefficient of skewness, and labels w…
• Kurtosis, Excess Kurtosis, and Tail WeightDivides the fourth central moment by the square of the second, subtracts 3 to give excess kurtosis, and says whether the tails …