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Topic: Gumbel (A, B) Sample skewness values by simulation
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Luis A. Afonso

Posts: 4,613
From: LIsbon (Portugal)
Registered: 2/16/05
Gumbel (A, B) Sample skewness values by simulation
Posted: Apr 6, 2014 3:25 PM
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The Fractiles of Gumbel (A,B) sample skewness sk=m3/(m2^1.5)

Based on that skewness of Gumbel (A, B) samples do have positive Skewness independently of the parameter´s values, but varying with sizes, I had shown that this characteristic can be used to separate from the Symmetric Populations such are the Normal/Gaussian ones.

G(A, B) sample skewness independence

quantiles are
_______________ 0.025__0.050__0.950__0.975__

n=100__G(0,1)___0.382__0.463__1.796__2.040
_____G(100,1)___0.385__0.462__1.793__2.038__
n=150__________0.493__0.564__1.734__1.941__
_______________0.492__0.564__1.738__1.942__
n=200__________0.564__0.628__1.680__1.870__
_______________0.563__0.629__1.677__1.873__
n=250__________0.612__0.673__1.643__ 1.813__
_______________0.608__0.669__1.639__1.804__
n=300__________0.652__0.708__1.610__1.773__
_______________0.550__0.706__1.608__1.763__

_______________0.025__0.050__0.950__0.975__

n=150__G(0,6)__ 0.498__0.573__1.727__1.938__
_______G(0,10)__0.501__0.569__1.725__1.941__
n=300__________0.648__0.708__1.612__1.764__
_______________0.649__0.703__1.601__1.754__
n=450________ 0.724__0.779__1.559__1.692__
______________ 0.730__0.776__1.552__1.678__
n=600_________ 0.766__0.815__1.497__1.595__
______________ 0.772__0.819__1.509__1.618__

From these results is worth to retain, 0.05 fractiles,

___ n=150___0.567
___ n=300__ 0.706
___ n=450__ 0.777
___ n=600__ 0.817

Epitomizing
It´s true that the parameter is constant along all defining parameter´s duo values, A, B, (see Note) but in what concerns finite samples they should be evaluate, sure. No surprising at all.

Note:
In error the Gumbel skewness at:
en.wikipedia.org/wiki/Gumbel_distributionwww.causascientia.org/?th_stat/Dists/Compendium.pdf
It should be as at
en.wikipedia.org/wiki/Gumbel_distribution
and the value is 1.12 approx.


Luis A. Afonso



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