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Re: Sample skew and kurtosis
- From: Brian Gough <bjg at network-theory dot co dot uk>
- To: Ben Klemens <klemens at hss dot caltech dot edu>
- Cc: gsl-discuss at sourceware dot org
- Date: Tue, 20 Mar 2007 12:00:18 +0000
- Subject: Re: Sample skew and kurtosis
- References: <20070315233956.GF1287@thebes.hss.caltech.edu>
At Thu, 15 Mar 2007 15:39:56 -0800,
Ben Klemens wrote:
> The same holds for the kurtosis and skew: if you have a sample and not a
> population, then the unbiased estimate is of the form \sum(...)/(n-1). But
> the above starts with 1/n, meaning we have population kurtosis normalized
> by sample variance squared.
>
> If we have to choose only one kurtosis and skew function, it should
> probably be the sample and not the population version. The fix is trivial:
> just return kurtosis * n/(n+1.0) at the end of kurtosis_m_sd, and
> similarly for skew.
Hello,
I originally looked at the formulas for unbiased estimators of
skewness and kurtosis and they were pretty complicated, so I went with
the simple definition used by Octave & Matlab.
--
Brian Gough