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Luis A. Afonso
Posts:
4,743
From:
LIsbon (Portugal)
Registered:
2/16/05


Where the lines go cross each other . . .
Posted:
Apr 8, 2014 6:53 PM


. . we find the minimum size two samples should have in order they are distinguishable through a common parameter. When we successively set sample sizes to increase the skewness of Gumbel and Normal Distributions behave as such: do decrease the 95% quantile of the former, increases the 5% of the latter. Obtained from 40´000 random sample each size. The following results are quite eloquent:
Skew 95% fractile__________Skew 5% fractile Normal/Gaussian___________Gumbel (A=0, B=1)
n=74____0.448_______________0.378____ n=76____0.441_______________0.393____ n=78____0.434_______________0.391____ n=80____0.431_______________0.397____ n=82____0.427_______________0.405____ n=84____0.422_______________0.416____* n=86____0.417_______________0.425____* n=88____0.412_______________0.427____ n=90____0.408_______________0.434____
Conclusion: in order that a Gumbel sample be distinct by its skewness from Gaussian ones one must chose sizes sample sizes somewhere at 84  86.
Repeating (as expected to perform in simulative procedures): Skew 95% fractile__________Skew 5% fractile Normal/Gaussian___________Gumbel (A=0, B=1)
n=74____0.449_______________0.379____ n=76____0.439_______________0.383____ n=78____0.437_______________0.396____ n=80____0.433_______________0.399____ n=82____0.425_______________0.411____ n=84____0.422_______________0.415____* n=86____0.416_______________0.422____* n=88____0.412_______________0.432____ n=90____0.412_______________0.436____
Luis A. Afonso



