[SciPy-user] Reference for scipy.stats.kurtosistest

[Kurt Smith]

On Wed, Mar 19, 2008 at 3:45 PM, Robert Kern <robert.kern at gmail.com> wrote:
>
> On Wed, Mar 19, 2008 at 3:17 PM, Kurt Smith <kwmsmith at gmail.com> wrote:
>  > Hello scipy-users (Specifically Robert Kern):
>  >
>  >  I'm making extensive use of scipy.stats.kurtosis, and noticed
>  >  'kurtosistest' which calculates the Z-score, and 2-tail Z-probability.
>  >   The source for this function is opaque to me -- what is being
>  >  calculated, and how?  Is there a reference to which you can refer me?
>
>  I don't know the details, but I believe the basic outline is this:
>  Gaussian PDFs have a particular kurtosis value, 3 (this is with
>  fisher=False; Fisher's kurtosis just subtracts 3 from the notional
>  value to talk about *excess* kurtosis). N samples drawn from a
>  Gaussian distribution will have an empirical kurtosis drawn from a
>  particular sampling distribution peaking at 3*(N-1)/(N+1). A suitable
>  transformation to that sampling distribution turns it into a standard
>  Gaussian distribution (sigma=1).
>
>  Apply that transformation to the empirical kurtosis obtained from the
>  dataset and you get a Z-score. A Z-score is just the number of sigmas
>  away from the mean you are on a Gaussian probability distribution.
>  Now, if you take this Z and add up the area under the standard
>  Gaussian <-|Z| and >+|Z|, you get the 2-tail Z probability. Basically,
>  this is the probability of getting an empirical kurtosis value at
>  least as extreme (in either direction) as the value that you actually
>  got if you took N samples from an actual Gaussian distribution.
>
>  Does that help?

Fantastic, thank you very much.

This has got to be one of the most helpful mailing lists I've come
across -- I ask for a reference, and you provide the explanation
instead.

Thanks again,

Kurt