John Randall wrote:
Kurtosis is normally defined as beta_2 as given in
http://mathworld.wolfram.com/Kurtosis.html
This appears to be the definition in statfns.ijs.
Yes, I think I understand now. The definition in J is for kurtosis
"proper", while kurtosis "excess" is also often used (in SPSS for example).
Wolfram MathWorld also gives the estimator for the kurtosis excess. I
should have checked Wolfram before posting here :-)
The variant definition may be an unbiased estimator from a sample.
I had the same suspicion (I couldn't think of any other possible reasons).
Thanks,
Tarmo
The
funny denominator is probably there for an analagous reason to estimating
the population variance from a sample:
S^2=(1/(n-1)) sum (x_i- xbar)^2
is an unbiased estimator of the population variance, but with denominator
n it is not.
Best wishes,
John
Tarmo Veskioja wrote:
A definition of kurtosis is given in statfns.ijs :
NB. kurtosis = 4th moment coefficient
kurtosis=: # * +/@(^&4)@dev % *:@ssdev
There seems to be a different definition of kurtosis given in the
Electronic Textbook from Statsoft:
http://www.statsoft.com/textbook/stathome.html
or more precisely at the bottom of page:
http://www.statsoft.com/textbook/glosi.html
Can anyone confirm and explain the difference?
Thanks,
Tarmo
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