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. So *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. Alecos Papadopoulos Athens University of Economics and Business, Greece Department of Economics cell:+30-6945-378680 fax: +30-210-8259763 skype:alecos.papadopoulos 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 of the > "moments" package for R, except that R gives total rather than excess > kurtosis. > > Allin Cottrell
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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. So Skewness Coefficient (this version is usually denoted "g1") Numerator: (1/n)(Σ(x_i - mean(X))^3) Denominator : [(1/n) Σ(x_i - mean(X))^2]^(3/2) (Excess) Kurtosis Coefficient (this version is usually denoted "g2") Numerator : (1/n)(Σ(x_i - mean(X))^4) Denominator : [(1/n) Σ[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. Alecos Papadopoulos Athens University of Economics and Business, Greece Department of Economics cell:+30-6945-378680 fax: +30-210-8259763 skype:alecos.papadopoulosOn 7/8/2014 19:00, [email protected] wrote: Yes. I might just add that our measures are in agreement with those of the "moments" package for R, except that R gives total rather than excess kurtosis. Allin Cottrell |
