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Formulas related to the extensive property are more naturally expressed in terms of the excess kurtosis. ... is the version found in Excel and several statistical ...
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
[6]: 115 The excess kurtosis of a distribution is the difference between its kurtosis and the kurtosis of a normal distribution, . [10]: 217 Therefore, the excess kurtosis of the geometric distribution is +.
The kurtosis is here defined to be the standardised fourth moment around the mean. The value of b lies between 0 and 1. [27] 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 ...
A function VAR.S in Microsoft Excel gives the unbiased sample variance while VAR.P is for population variance. ... where κ is the kurtosis of the distribution and ...
Based on the formula ... is the version found in Excel ... D'Agostino's K-squared test is a goodness-of-fit normality test based on sample skewness and sample kurtosis.
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The values γ 1 and γ 2 are the random variable's skewness and (excess) kurtosis respectively. The value(s) in each set of brackets are the terms for that level of polynomial estimation, and all must be calculated and combined for the Cornish–Fisher expansion at that level to be valid.