QuartileSkewness

QuartileSkewness[data]
gives the coefficient of quartile skewness for the elements in list.
QuartileSkewness[data,{{a,b},{c,d}}]
uses the quantile definition specified by parameters a, b, c, d.
QuartileSkewness[dist]
gives the coefficient of quartile skewness for the distribution dist.
Details


- With {q1/4,q2/4,q3/4}=Quartiles[data], QuartileSkewness[data] is equivalent to
.
- A positive value of quartile skewness indicates the median
is closer to the lower quartile
than the upper quartile
.
- A negative value of quartile skewness indicates the median
is closer to the upper quartile
.
-
- Common choices of parameters {{a,b},{c,d}} include:
-
{{0, 0}, {1, 0}} inverse empirical CDF (default) {{0, 0}, {0, 1}} linear interpolation (California method) {{1/2, 0}, {0, 0}} element numbered closest to p n {{1/2, 0}, {0, 1}} linear interpolation (hydrologist method) {{0, 1}, {0, 1}} mean‐based estimate (Weibull method) {{1, -1}, {0, 1}} mode‐based estimate {{1/3, 1/3}, {0, 1}} median‐based estimate {{3/8, 1/4}, {0, 1}} normal distribution estimate - The default choice of parameters is {{0,0},{1,0}}.
- The data can have the following additional forms and interpretations:
-
Association the values (the keys are ignored) » SparseArray as an array, equivalent to Normal[data] » QuantityArray quantities as an array » WeightedData based on the underlying EmpiricalDistribution » EventData based on the underlying SurvivalDistribution » TimeSeries, TemporalData, … vector or array of values (the time stamps ignored) » Image,Image3D RGB channels values or grayscale intensity value » Audio amplitude values of all channels »
Examples
open allclose allBasic Examples (2)
Scope (18)
Basic Uses (8)
Exact input yields exact output:
Approximate input yields approximate output:
Compute results using other parametrizations:
Find the quartile skewness for WeightedData:
Find the quartile skewness for EventData:
Find the quartile skewness for TemporalData:
Find the quartile skewness of TimeSeries:
Array Data (5)
QuartileSkewness for a matrix gives columnwise ranges:
QuartileSkewness for a tensor gives columnwise medians at the first level:
When the input is an Association, QuartileSkewness works on its values:
SparseArray data can be used just like dense arrays:
Find quartile skewness of a QuantityArray:
Image and Audio Data (2)
Applications (6)
Zero QuartileSkewness indicates the median is equally distant from the remaining quartiles:
Positive QuartileSkewness indicates that the median is closer to the lower quartile:
Negative QuartileSkewness indicates that the median is closer to the upper quartile:
Obtain a robust estimate of asymmetry when extreme values are present:
Measures based on the Mean are heavily influenced by extreme values:
This time series contains the number of steps taken daily by a person during a period of five months:
Analyze whether the step distribution is skewed toward the lower or the upper quartile:
The histogram of the frequency of daily counts shows that the median is closer to the upper quartile:
Find the quartile skewness for the heights of children in a class:
Negative quartile skewness indicates that the median is closer to the lower quartile:
Properties & Relations (3)
QuartileSkewness is a function of linearly interpolated Quantile values:
QuartileSkewness is a function of quartiles:
QuartileSkewness is a function of the median, first quartile and a dispersion measure:
Possible Issues (1)
QuartileSkewness requires numeric values:

Neat Examples (1)
The distribution of QuartileSkewness estimates for 50, 100 and 300 samples:
Text
Wolfram Research (2007), QuartileSkewness, Wolfram Language function, https://reference.wolfram.com/language/ref/QuartileSkewness.html (updated 2023).
CMS
Wolfram Language. 2007. "QuartileSkewness." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/QuartileSkewness.html.
APA
Wolfram Language. (2007). QuartileSkewness. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/QuartileSkewness.html