> Phil Steitz wrote:
> > No, you are not missing anything. What you are suggesting should
> > work fine, with similar change for getResult.
> >
> > A little nit -- I would prefer to use a boolean for the property
> > (unless there are more than two values) and not rely on the *value*
> > of the int constant (flag) in the computation. Alternatively,
> > the property could be a float/double, with its value used directly
> > -- but I honestly don't know how meaningful / useful that property
> > would be.
> Well, I did not figure it out completely, but somewhere, I feel we
> might need that with weighted values.....
Do you think a double-valued property named "biasReduction" with a
default value of 1 would be appropriate then? Have you ever seen this
used in practice ("partial" bias-reduction)?
> Another stray though goes towards skewness and kurtois estimates, do
> they use sometimes bias reduction?
Yes, we use bias-corrected formulas for these and it is less obvious how
to measure / configure the bias reduction for skewness and kurtosis (see
below). I also do not know if the "population" versions have lower MSE
or there are other practical reasons that people would want to use them
in some cases. Does anyone know of applications of these?
> If so, those might be using 2 and 3 (which I have seen for a kurtois
> calculation somewhere recently).
Could be what you are referring to is a "centering" constant (3) that
is subtracted to scale the statistic so that N(0,1) has Kurtosis = 0. This is
unrelated to bias reduction. The (definitional) formula that we use for Kurtosis is:
{[n(n+1) / (n -1)(n - 2)(n-3)] sum[(x_i - mean)^4] / std^4 } - [3(n-1)^2
/ (n-2)(n-3)]
The "population" version would be:
sum[(x_i - mean)^4] / (n * sigma^4) - 3
where sigma is the "population" standard deviation. It is not obvious how to
parameterize the bias reduction.
I guess my inclination at this point is to make the property
boolean-valued for Variance, StandardDeviation and omit it altogether
(for now) for Skewness and Kurtosis. Is everyone OK with this?
Also, since we agreed earlier to avoid boolean / int flags in APIs, I
would prefer to either make this a (writable) property instead of
overloading the getResult and evaluate methods to take the flag as a
parameter. Do we all agree?
If there are no objections, I will make these changes.
Phil
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