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.papadopoulos
On 7/8/2014 19:00,
gretl-users-request@lists.wfu.edu wrote: