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Re: Variance of Skewness and Kurtosis
Posted:
Jun 18, 2012 9:02 PM
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On Fri, 15 Jun 2012 19:00:04 -0700 (PDT), Havilah
<stefanie1920@gmail.com> wrote:
>You are not entirely clear.
>>
>> (1) if you have 400000 values of skewness then you could just use these to
>> estimate the variance or percentage points of the sampling distribution of
>> the skewness.
>
>Thanks for your suggestions. I have about 400,000 data sets and each have a kurtosis. Although I set the algorithm to produce a kutosis of 7 for each data set, I suspect the fluctuation I am seeing is too much. Something seems off. For example, although I set the kurtosis to 7, I did a quick check and found that most of the datasets had a kurtosis between 5 and 12. Although 7 falls in that interval, intuitively that range seems off. I would expect a range of about 6 to 8.
I don't know what your distribution looks like, but
kurtosis of 7 indicates a fairly sharp peak. However,
I found an odd reference which shows that a Pearson
Type VII distribution, kurtosis = 4, is not greatly
different from the curve with kurtosis "infinite".
See
http://en.wikipedia.org/wiki/User:MarkSweep/work
- This citation looks like a work-sheet for some regular Wiki
contributor, so I don't know how permanent it may be.
(Last modified 21 September, 2011). Oh, the graph is
also in the article on Pearson distributions, and the article
on kurtosis.
If there is not *much* difference in curves for 4 or infinite,
then you must have pretty large samples in order to
keep your range between 5 and 12. The article on kurtosis
seems to show that the difference is not the height of the
peak, but the relative densities of the (rather thin) tails -
looking at the graph of the log of densities.
--
Rich Ulrich
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