# 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**

### Real number

**realrealsreal-valued**

### 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**

### 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.