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Excess kurtosis, typically compared to a value of 0, characterizes the “tailedness” of a distribution. A univariate normal distribution has an excess kurtosis of 0. 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 Laplace distribution has a kurtosis of 6 and weak exponential tails, but a larger 4th L-moment ratio than e.g. the student-t distribution with d.f.=3, which has an infinite kurtosis and much heavier tails. As an example consider a dataset with a few data points and one outlying data value.
The kurtosis is here defined to be the standardised fourth moment around the mean. The value of b lies between 0 and 1. [26] The logic behind this coefficient is that a bimodal distribution with light tails will have very low kurtosis, an asymmetric character, or both – all of which increase this coefficient. The formula for a finite sample ...
For example, if the HSV color space is used, this means that for each of the images, 9 features in total will be computed (the first three order moments for the Hue, Saturation, and Value channels). Calculating the similarity score - After computing the color moments the weights for each of the moments in the d m o m ( H , I ) {\displaystyle d ...
The plot of excess kurtosis as a function of the variance and the mean shows that the minimum value of the excess kurtosis (−2, which is the minimum possible value for excess kurtosis for any distribution) is intimately coupled with the maximum value of variance (1/4) and the symmetry condition: the mean occurring at the midpoint (μ = 1/2).
Most simply, they can be estimated in terms of the higher moments, using the method of moments, as in the skewness (3rd moment) or kurtosis (4th moment), if the higher moments are defined and finite. Estimators of shape often involve higher-order statistics (non-linear functions of the data), as in the higher moments, but linear estimators also ...
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.
In statistics, the Jarque–Bera test is a goodness-of-fit test of whether sample data have the skewness and kurtosis matching a normal distribution. The test is named after Carlos Jarque and Anil K. Bera. The test statistic is always nonnegative. If it is far from zero, it signals the data do not have a normal distribution.