On 24/05/2013 21:32, Rich Ulrich wrote: > On Fri, 24 May 2013 19:39:15 +0200, Cristiano <cristiapi@NSgmail.com> > wrote: > >> I calculate the skewness and the kurtosis from a set of real numbers >> (distribution unknown) using the formulas: >> >> http://mvpprograms.com/help/mvpstats/distributions/SkewnessCriticalValues >> >> http://mvpprograms.com/help/mvpstats/distributions/KurtosisCriticalValues >> >> 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?