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From Phil Steitz <p...@steitz.com>
Subject Re: [math] Only sample variances?
Date Mon, 16 Aug 2004 00:02:11 GMT
Mark R. Diggory wrote:
> Yes, at the UnivariateStatistic level, these would need to be new 
> classes. My question as well is "Does it apply as well to higher order 
> moments?"

In theory, yes, though I have never seen non-bias-corrected versions of 
Skewness and Kurtosis used.  The current formulas are all defined for the 
most common use case where the data represent a sample from a population 
whose true distribution and associated parameters are unknown.population 
The formulas that we use provide unbiased estimators for population 
parameters in this case.  This is explained fairly well for the Variance here:
http://mathworld.wolfram.com/Variance.html
and for Skewness and Kurtosis here:
http://mathworld.wolfram.com/k-Statistic.html

The "Population Variance" is useful when the data *are* the population 
(i.e. the distribution is discrete and there is no sampling going on).  I 
am not aware of use cases where Skewness and Kurtosis are useful in 
analyzing full population data or other uses for the non-bias-corrected 
versions of these.  These could exist, I am just not aware of them.

> 
> Maybe we should place everything into the following packages:

I don't think we need yet another subpackage.

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