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In analyzing Miller's spreadsheet, I realized his book displays the formulas for co-skew and co-kurtosis incorrectly. There is a thematic confusion between the (unstandardized) cross-central moments versus "skew" and "kurtosis" which are standardized: 3.42 and 3.47 forget to divide by N, so they aren't the

Here is the draft XLS, in case anybody wants to take a look @ http://trtl.bz/coskew-cokurt

(same as this dropbox file)

*expected*values of (X - mu)^m, they are instead the sums. To review:- The 3rd central moment (aka, moment about mean) = E[X - mu]^3, so if you aren't using a probability distribution (but rather a sample), you need to take the average of the sum of [X-mu]^3 to get the Expected[X-mu]^3. But that's a "raw" or un-standardized 3rd central moment; in the same way that it's hard to make sense of the units of a variance b/c variance is the un-standardized second central moment E[X - mu]^2
- Skew, then, is the standardized 3rd central moment, S = E[X - mu]^3/sigma(X)^3 = 3rd central moment/(to standardize)

Kurtosis, then, is the standardized 4th central moment, K = E[X - mu]^4/sigma(X)^4 - So 3.47 is incorrect: if it's a sample, in needs to divide the sum by (n). If it's a probability distribution, then to the same effect, the formula needs to be K = Sigma[
**p(i)***[x(i) - mu]^4]/sigma^4. And if we have probabilities, then we don't need the sample adjustment.

Here is the draft XLS, in case anybody wants to take a look @ http://trtl.bz/coskew-cokurt

(same as this dropbox file)

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