Looking for help with an algorithm ..

[David Patrick]

As stated in my previous post, I am dealing with a file with around 100
million samples and I'd like to only have to pass through the data once and
I can not sort the data.

I'd like to be able to perform the following calculations on the data, but
as the formulas stand they would require me to take two passes at the data
.. the first pass to determine the mean and the second pass to calculate the
actual value using the mean to determine the ( x_j - <x> ) portion.

The Formula's ( taken from Numerical Recipes in C )

1) Skew = 1 N
------- Sum ( ( x_j - <x> ) / stdev ) ^3
N j=1

and

1) Kurtosis = 1 N
------- Sum ( ( x_j - <x> ) / stdev ) ^4
N j=1

the Numerical Recipes book goes on to say that "Many textbooks use the
binomial theorem to expand out the definitions into sums of various powers
of the data, e.g, the familiar ... " and then it goes on to give an example
using the formula for the variance function. As I have stated in another
post, "Can Someone explain this?", I couldnt reproduce the results for the
variance function so I know applying the binomial theorm to 3rd and 4th
power is way out of my league. So basically I am asking for your help and
kindness .. does anybody have the above formulas in a different from that
is "expressed as sums of various powers of the data " ? (see my "Can Someone
explain this?" post for the example of the variance function expressed as a
sums of various powers of the data )

Eagerly awaiting any help,

Dave