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In statistics and probability theory, the nonparametric skew is a statistic occasionally used with random variables that take real values. [1] [2] 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 is the mean, is the median, and 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 ...
Nonparametric statistics is a type of statistical analysis that makes minimal assumptions about the underlying distribution of the data being studied. Often these models are infinite-dimensional, rather than finite dimensional, as in parametric statistics. [1]
Nonparametric skew; Non-parametric statistics; Non-response bias; Non-sampling error; Nonparametric regression; Nonprobability sampling; Normal curve equivalent; Normal distribution; Normal probability plot – see also rankit; Normal score – see also rankit and Z score; Normal variance-mean mixture; Normal-exponential-gamma distribution ...
The value of the nonparametric skew. of this distribution lies between 0 and 0.31. [10] [11] The lower limit is approached when the normal component dominates, and the upper when the exponential component dominates.
However, if the distribution has skew, trimmed estimators will generally be biased and require adjustment. For example, in a skewed distribution, the nonparametric skew (and Pearson's skewness coefficients) measure the bias of the median as an estimator of the mean.
The sample skewness g 1 and kurtosis g 2 are both asymptotically normal. However, the rate of their convergence to the distribution limit is frustratingly slow, especially for g 2 . For example even with n = 5000 observations the sample kurtosis g 2 has both the skewness and the kurtosis of approximately 0.3, which is not negligible.
However, if the distribution has skew, symmetric L-estimators will generally be biased and require adjustment. For example, in a skewed distribution, the nonparametric skew (and Pearson's skewness coefficients) measure the bias of the median as an estimator of the mean.