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Luis A. Afonso
Posts:
4,518
From:
LIsbon (Portugal)
Registered:
2/16/05
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Cramer-von Mises statistics:to standardize or not?
Posted:
Oct 13, 2012 7:37 PM
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Cramer-von Mises statistics: to standardize or not?
From the paper:
The Exact and Asymptotic Distribution of Cramer- von Mises Statistics
Authors: S. Gsorgo, J. J. Faraday (Michigan, USA, 1994)
I wonder if the authors had considered standardizing the samples before to evaluate the test statistics:
____T= 1/(12*n) * Sum [(2*k-1)/(2*n) - Phi(k)]^2
for normal sample, n size, Phi( ) the inverse Normal, the sum performed for the ordered sample as usual.
My evaluations, without standardizations were:
____n= 10, quantile 0.50, Table= 0.12068
____My observed frequencies:
____10´000 samples 0.509; 40´000, 0.501.
____n= 50, quantile 0.95, Table= 0.45986
____
____10´000 samples 0.9499; 40´000, 0.9502.
It is clear that standardization (subtract the sample mean then divide by the standard deviation) weren?t performed.
Luis A. Afonso
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