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Topic: What Karl Pearson dared not to do . . .
Replies: 0

 Luis A. Afonso Posts: 4,758 From: LIsbon (Portugal) Registered: 2/16/05
What Karl Pearson dared not to do . . .
Posted: Nov 18, 2013 1:34 PM

What Karl Pearson dared not to do . . .

Very likely Jarque and Bera following the Pearson´s test on normality and thought that were most smart in adding the Skewness and Kurtosis estimators after normalizing (Kurtosis excess) and squaring them using the variances 6/n and 24/n. Once getting the squares of two normal r.v, each one follows a one-degree of freedom chi-squared law, the sum a two-degrees. . . . Et voilà!___ (and so there)! .

Remember that Pearson even then defined:
___b1= m3/(m2^3/2)___b2= m4/(m2^2)
But the decision was depending the critical values(cv),
___Reject if |b1|> cv1(1-alpha/2), or
_____ if b2 outside [cv2(alpha/2, cv2(1-alpha/2]

J-B did not refrain to go further___and crash . . .

See:
www.sfu.ca/~poitras/el\$.pdf

Luis A. Afonso