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Re: st: Query..

From   Nick Cox <>
To   "" <>
Subject   Re: st: Query..
Date   Wed, 17 Apr 2013 01:57:02 +0100

On this front, kurtosis is even more curious than almost any account allows.

Kaplansky, I.  1945. A common error concerning kurtosis.  Journal,
American Statistical
        Association 40: 259 only.

gave specific examples of density functions with kurtosis above and
below 3 with contrary  tail behaviour. The whole  kit and caboodle is
bundled in a program -kaplansky- (SSC) that draws the graphs for you.
You can also get the full tale (tail?) by typing

. ssc type kaplansky.hlp

It is to be surmised that Kaplansky's work on kurtosis (he later
become a famous algebraist working with groups, rings, fields, and so
forth) was somehow part of the U.S. war effort, but nevertheless
publishable. In an odd parallel the British-born
mathematician-turned-physicist Freeman Dyson also worked on the
statistics of air force campaigns and published a theorem on kurtosis
in the Journal of the Royal Statistical Society in 1943.

I am not making this up, you know, as was famously said in an exegesis
of the Wagnerian Ring cycle.


On 16 April 2013 23:43, David Hoaglin <> wrote:

> On page 253, the discussion of values of kurtosis that depart from
> that for the normal distribution (3.00) is reversed: "A value of less
> than 3.00 means that the tails are too thick (hence, too flat in the
> middle), and a value of greater than 3.00 means that the tails are too
> thin (hence, too peaked in the middle)."  In fact, heavier-than-normal
> tails correspond to kurtosis > 3, and lighter-than-normal tails
> correspond to kurtosis < 3.
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