For what is worth, I was able to determine through numerical
experiments, that Gretl uses the "Fisher-Pearson" formulas for
calculating the skewness and excess kurtosis coefficients.
This essentially means that for the calculation of these coefficients,
all sample means involved (/even/ the sample variance/standard
deviation) are calculated using the factor (1/n), and that no
bias-correction terms appear.
I am writing this informatively - I have no settled opinion on which
alternative formula should be preferred.
*Skewness* Coefficient (this version is usually denoted "g1")
Numerator: (1/n)(?(x_i - mean(X))^3)
Denominator : [(1/n)?(x_i - mean(X))^2]^(3/2)
*(Excess) Kurtosis *Coefficient (this version is usually denoted "g2")
Numerator : (1/n)(?(x_i - mean(X))^4)
Denominator : [(1/n)?[x_i - mean(X)]^2]^2
and we further subtract "3" after we calculate the ratio to obtain the
"excess" over the kurtosis of the normal distribution.
References for the names and presentations of various alternatives
Joanes, D. N., & Gill, C. A. (1998). Comparing measures of sample
skewness and kurtosis. /Journal of the Royal Statistical Society: Series
D (The Statistician)/, /47/(1), 183-189.
Doane, D. P., & Seward, L. E. (2011). Measuring skewness: a forgotten
statistic. /Journal of Statistics Education/, /19/(2), 1-18.
Athens University of Economics and Business, Greece
Department of Economics
On 7/8/2014 19:00, gretl-users-request(a)lists.wfu.edu wrote:
Yes. I might just add that our measures are in agreement with those
"moments" package for R, except that R gives total rather than excess