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Topic: Cramer-von Mises statistics:to standardize or not?
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Luis A. Afonso

Posts: 4,758
From: LIsbon (Portugal)
Registered: 2/16/05
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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