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Topic: Skewness and kurtosis p-values
Replies: 11   Last Post: May 28, 2013 6:50 AM

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Posts: 60
Registered: 12/7/12
Re: Skewness and kurtosis p-values
Posted: May 24, 2013 6:21 PM
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On 24/05/2013 21:32, Rich Ulrich wrote:
> On Fri, 24 May 2013 19:39:15 +0200, Cristiano <>
> wrote:

>> I calculate the skewness and the kurtosis from a set of real numbers
>> (distribution unknown) using the formulas:
>> I usually need to check whether the calculated skewness and kurtosis are
>> in good agreement with the expected values for a normal or uniform
>> distribution; I need a p-value.
>> I'm trying to replicate (via simulation) the p-values (alpha) presented
>> in that site, but I get different values. For example, for n= 7 and
>> alpha= 0.1, for the skewness I get 1.169 instead of 1.307.
>> For the skewness I do the following:
>> 1) generate a random number x_i in N(0,1)
>> 2) if x_i < 0 discard the number
>> 3) for n= 7 I do the above steps until i = 1428571
>> 4) calculate the 95th percentile (for alpha= 0.1) of the x's.
>> Does anybody know where I could be wrong?

> My tentative guess is that you cut-and-paste'd your
> steps from some wrong source.

I wrote a C++ working program; I "extracted" the steps from there.

> Discarding negative numbers has nothing to do with
> computing skewness, so far as I can imagine.

The steps are a bit inaccurate.
I meant that I discard the skewness < 0.

> Somewhere in the steps, you should "compute skewness."
> 1) Draw 7; compute skewness; save.
> 2) Repeat 100,000 times.
> 3) Show 5% and 95% points (should be nearly the same absolute values).
> 3) Repeat 10 times.

Yes, I do that, but to be more precise:
1) Draw 7; compute skewness;
2) if skewness < 0 discard the value, else save.
3) Repeat 100,000 times.
4) Show 95% points.
5) Repeat until the confidence limit is good.

The reason to discard skewness < 0 is that I need to calculate only a
critical value for the skewness (the distribution must be exactly
symmetrical); if I get 5th percentile = -0.123 and 95th percentile =
.124, which critical value should I take?


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