| Question about MOMENT [message #4786] |
Wed, 26 July 1995 00:00 |
ECSPRS
Messages: 6
Registered: November 1994
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Junior Member |
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Hi again.
There's something in the MOMENT function I don't think fits with the online
documentation. When calculating the variance the online help defines it as;
1 [ N-1 1 [ N-1 ] ]
Variance = ---- [Sigma (Xi-Xbar)^2 - --- [ Sigma (Xi-Xbar) ]^2 ]
N-1 [ i=0 N [ i=0 ] ]
where Xi is data points, Xbar is the mean, N number of points.
Now in the function code of MOMENT.PRO (in \IDL40\LIB) variance is calculated
the following way;
var1 = total((x - mean)^2) / (nx-1.0)
var2 = (total((x-mean)^2) - ((total((x-mean)))^2)/nx)/(nx-1.0)
var = (var1 + var2)/2.0
sdev = sqrt(var) ; standard deviation
Now var1 is obviously the first term in the above equation. What I couldn't
figure was why that term also appears in var2, along with the second term,
until I saw the third line which adds and then divides by 2 to get var. So to
rewrite the IDL code as equations that means;
var = Sigma(Xi - Xbar)^2 Sigma(Xi - Xbar)^2 (Sigma(Xi - Xbar))^2
------------------ + ------------------- - --------------------
2(N-1) 2(N-1) 2N(N-1)
(dropping all the sigma extra bits)
So, point (1), the second term has now been divided by a factor of 2, unlike
what appears in the documentation, and point (2) why go to all the
computational effort of calculating term 1 twice just so you can halve it and
add them together? The rest of the MOMENT code doesn't show any other use for
individual var1 and var2 parts. As far as I can see lines 1 and 3 of the above
code should be dropped and var2 is the result we're after.
Comments, flames, anyone?
Paul
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