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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


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



