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Re: st: How to calculate kurtosis on left tail and right tail separately?


From   Nick Cox <njcoxstata@gmail.com>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: How to calculate kurtosis on left tail and right tail separately?
Date   Sun, 14 Apr 2013 11:16:16 +0100

Quite what do you mean by the kurtosis of each tail?

Kurtosis is a quantity defined for an entire distribution; you _could_
calculate kurtosis conditionally for e.g. (values > mean) and (values
< mean) but the results won't be comparable with kurtosis for the
entire distribution.

You could also mirror each tail by its reflection, e.g. the left half
and itself reflected is

cond(value > mean, value - mean, mean - value)

and conversely for the right half you could get

cond(value < mean, value - mean, mean - value)

Note that now you are now calculating kurtosis for about 13 values,
doubled up, not a good idea, as previously commented.

Nick
njcoxstata@gmail.com

On 14 April 2013 06:22, Mengjia wrote:

> I wish to test the kurtosis difference between female- and male-managed funds return to examine the possibility of great gain and great loss separately. The current code leads me to an overall kurtosis value on both tails. Is there any way to calculate the kurtosis value on each tail?
>
> My current code:
> bys Fund Year, egen kurt = kurt (Return)
>
> For each fund at each year, 52 weekly returns are provided.

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