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The distribution is said to be left-skewed, left-tailed, or skewed to the left, despite the fact that the curve itself appears to be skewed or leaning to the right; left instead refers to the left tail being drawn out and, often, the mean being skewed to the left of a typical center of the data. A left-skewed distribution usually appears as a ...
When the smaller values tend to be farther away from the mean than the larger values, one has a skew distribution to the left (i.e. there is negative skewness), one may for example select the square-normal distribution (i.e. the normal distribution applied to the square of the data values), [1] the inverted (mirrored) Gumbel distribution, [1 ...
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 .
The Lévy skew alpha-stable distribution or stable distribution is a family of distributions often used to characterize financial data and critical behavior; the Cauchy distribution, Holtsmark distribution, Landau distribution, Lévy distribution and normal distribution are special cases. The Linnik distribution; The logistic distribution
Type I has also been called the skew-logistic distribution. Type IV subsumes the other types and is obtained when applying the logit transform to beta random variates. Following the same convention as for the log-normal distribution , type IV may be referred to as the logistic-beta distribution , with reference to the standard logistic function ...
The skew normal distribution is another distribution that is useful for modeling deviations from normality due to skew. Other distributions used to model skewed data include the gamma , lognormal , and Weibull distributions, but these do not include the normal distributions as special cases.
where is the beta function, is the location parameter, > is the scale parameter, < < is the skewness parameter, and > and > are the parameters that control the kurtosis. and are not parameters, but functions of the other parameters that are used here to scale or shift the distribution appropriately to match the various parameterizations of this distribution.
Negative excess kurtosis indicates a platykurtic distribution, which doesn’t necessarily have a flat top but produces fewer or less extreme outliers than the normal distribution. For instance, the uniform distribution (ie one that is uniformly finite over some bound and zero elsewhere) is platykurtic. On the other hand, positive excess ...