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Larger kurtosis indicates a more serious outlier problem, and may lead the researcher to choose alternative statistical methods. D'Agostino's K-squared test is a goodness-of-fit normality test based on a combination of the sample skewness and sample kurtosis, as is the Jarque–Bera test for normality.
Kurtosis risk applies to any kurtosis-related quantitative model that assumes the normal distribution for certain of its independent variables when the latter may in fact have kurtosis much greater than does the normal distribution. Kurtosis risk is commonly referred to as "fat tail" risk. The "fat tail" metaphor explicitly describes the ...
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 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.
Robust estimation typically attempts to correct the problem by adjusting the normal theory model χ 2 and standard errors. [9] For example, Satorra and Bentler (1994) recommended using ML estimation in the usual way and subsequently dividing the model χ 2 by a measure of the degree of multivariate kurtosis. [11]
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Few explanations were suggested to explain these phenomena. It was argued that they are heavily dependent on density and less on numerosity. Also, it was suggested that numerosity may be correlated with kurtosis and that the results may be better explained in terms of texture density such that only dots falling within the spatial region where the test is displayed effectively adapt the region.