Re: skewness and kurtosis
From: Glen (glenbarnett_at_geocities.com)
Date: 08/18/04
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Date: 17 Aug 2004 19:18:46 -0700
Stan Brown <the_stan_brown@fastmail.fm> wrote in message news:<MPG.1b85341dec1c2d1d98c82d@news.odyssey.net>...
> A distribution that is not symmetric is skewed. Skewness is a number
> that measures how un-symmetric the distribution is.
Note that the usual 3rd-moment-based measure of "skewness" is
/intended/ to be "a number that measures how un-symmetric the
distribution is". That doesn't quite make it one.
For example, if the 3rd (central) moment is zero, the distribution
may nevertheless be asymmetric.
Don't take this as a call to abandon the moment-measure; like all the
measures of skewness it has its uses and its problems.
The 4th-moment (kurtosis) measure also has problems if you try to
look at it purely as a measure of peakedness or heavy-tailedness.
Similar comments apply.
In general, if you want to measure some not-completely-clearly
defined aspect of a distribution like "skewness", you need to
consider the behaviour you want it to have in a variety of
circumstances and then choose a measure that reflects what
you want it to do.
Glen
- Previous message: Richard Ulrich: "Re: QUERY: Sample proportion and prediction"
- In reply to: Stan Brown: "Re: skewness and kurtosis"
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- Reply: Herman Rubin: "Re: skewness and kurtosis"
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