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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 onedegree of freedom chisquared law, the sum a twodegrees. . . . 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(1alpha/2), or _____ if b2 outside [cv2(alpha/2, cv2(1alpha/2]
JB did not refrain to go further___and crash . . .
See: www.sfu.ca/~poitras/el$.pdf
Luis A. Afonso



