Nonparametric skew

In statistics and probability theory, the nonparametric skew is a statistic occasionally used with random variables that take real values.wikipedia
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Skewness

skewedskewskewed distribution
It is a measure of the skewness of a random variable's distribution—that is, the distribution's tendency to "lean" to one side or the other of the mean.
In the older notion of nonparametric skew, defined as where \mu is the mean, \nu is the median, and \sigma is the standard deviation, the skewness is defined in terms of this relationship: positive/right nonparametric skew means the mean is greater than (to the right of) the median, while negative/left nonparametric skew means the mean is less than (to the left of) the median.

Exponentially modified Gaussian distribution

exGaussian distributionExponentially modified Gaussianexponentially modified normal distribution
*Exponentially modified Gaussian distribution:
The value of the nonparametric skew

Statistics

statisticalstatistical analysisstatistician
In statistics and probability theory, the nonparametric skew is a statistic occasionally used with random variables that take real values.

Probability theory

theory of probabilityprobabilityprobability theorist
In statistics and probability theory, the nonparametric skew is a statistic occasionally used with random variables that take real values.

Statistic

sample statisticempiricalmeasure
In statistics and probability theory, the nonparametric skew is a statistic occasionally used with random variables that take real values.

Random variable

random variablesrandom variationrandom
In statistics and probability theory, the nonparametric skew is a statistic occasionally used with random variables that take real values.

Real number

realrealsreal-valued
In statistics and probability theory, the nonparametric skew is a statistic occasionally used with random variables that take real values.

Probability distribution

distributioncontinuous probability distributiondiscrete probability distribution
It is a measure of the skewness of a random variable's distribution—that is, the distribution's tendency to "lean" to one side or the other of the mean.

Mean

mean valuepopulation meanaverage
It is a measure of the skewness of a random variable's distribution—that is, the distribution's tendency to "lean" to one side or the other of the mean. where the mean, median and standard deviation of the population have their usual meanings.

Nonparametric statistics

non-parametricnonparametricnon-parametric statistics
Its calculation does not require any knowledge of the form of the underlying distribution—hence the name nonparametric.

Scale parameter

scalerate parameterestimation
It has some desirable properties: it is zero for any symmetric distribution; it is unaffected by a scale shift; and it reveals either left- or right-skewness equally well.

Sample (statistics)

samplesamplesstatistical sample
In statistical samples it has been shown to be less powerful than the usual measures of skewness in detecting departures of the population from normality.

Power (statistics)

statistical powerpowerpowerful
In statistical samples it has been shown to be less powerful than the usual measures of skewness in detecting departures of the population from normality.

Statistical population

populationsubpopulationsubpopulations
In statistical samples it has been shown to be less powerful than the usual measures of skewness in detecting departures of the population from normality.

Normal distribution

normally distributednormalGaussian
In statistical samples it has been shown to be less powerful than the usual measures of skewness in detecting departures of the population from normality.

Median

averagesample medianmedian-unbiased estimator
where the mean, median and standard deviation of the population have their usual meanings.

Affine transformation

affineaffine functionaffine transformations
Under an affine transformation of the variable (X), the value of S does not change except for a possible change in sign.

Absolute value

modulusabsolutemagnitude
The bounds of this statistic ( ±1 ) were sharpened by Majindar who showed that its absolute value is bounded by

Variance

sample variancepopulation variancevariability
where X is a random variable with finite variance, E is the expectation operator and Pr is the probability of the event occurring.

Expected value

expectationexpectedmean
where ν 0 is any median and E is the expectation operator.

Quantile function

quantileinverse distribution functionnormal quantile function
where x q is the q th quantile.

Order statistic

order statisticsorderedth-smallest of items
For a finite sample with sample size n ≥ 2 with x r is the r th order statistic, m the sample mean and s the sample standard deviation corrected for degrees of freedom,

Standard deviation

standard deviationssample standard deviationsigma
where the mean, median and standard deviation of the population have their usual meanings. For a finite sample with sample size n ≥ 2 with x r is the r th order statistic, m the sample mean and s the sample standard deviation corrected for degrees of freedom,

Student's t-distribution

Student's ''t''-distributiont''-distributiont-distribution
where n is the sample size, is distributed as a t distribution.

Yulia Gel

Gel
Assuming a symmetric underlying distribution, a modification of S was studied by Miao, Gel and Gastwirth who modified the standard deviation to create their statistic.