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Topic: Variance of Skewness and Kurtosis
Replies: 8   Last Post: Jun 19, 2012 2:36 PM

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 Richard Ulrich Posts: 2,795 Registered: 12/13/04
Re: Variance of Skewness and Kurtosis
Posted: Jun 18, 2012 9:02 PM

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.
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

Date Subject Author
6/15/12 Havilah
6/15/12 Richard Ulrich
6/15/12 Havilah
6/15/12 David Jones
6/15/12 Havilah
6/15/12 Ray Koopman
6/16/12 David Jones
6/18/12 Richard Ulrich
6/19/12 Havilah