Sometimes the excess curtose over the normal
is computed, so the result is zero for the
normal.
Formulas(estimates) are:
asimmetry:
1/(n-1)(s^3) \sum(X_i-Xbar)^3
curtosis:
1/(n-1)(s^4) \sum(X_i-Xbar)^4,
where n is the sample size, s^2 the sample variance
and Xbar the sample mean.
For samples from the normal, the first statistics
is approximately normal, with mean 0 and variance 6/n
and the second statistics is approximately normal,
with mean 3 and variance 24/n. These are useful for a
test for normality (Jarque and Bera, 1981.)
Best,
Pedro Morettin
U. of Sao Paulo, Brasil
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