[SciPy-user] skew Gaussian distribution

Gary Pajer gary.pajer@gmail....
Thu Aug 23 14:53:18 CDT 2007


On 8/23/07, David Goldsmith <David.L.Goldsmith@noaa.gov> wrote:
>
> Ah, then I may be able to help you in two ways.  First, my Google search
> turned up:
>
> http://azzalini.stat.unipd.it/SN/
>
> Visit the "very brief account" link thereon,



Indeed, on the "very brief account page" a skewed normal is defined as
norm.pdf(x) * norm.cdf(a*x)

which seems to work quite nicely.
thanks


but also note on the main
> page the passage titled "A pioneer" which hints at a possible "physical"
> basis for these distributions in nature; I didn't dig any deeper than
> that, but it seems worthwhile to assess whether the family of
> distributions he is discussing might "properly" represent your
> experimental population.
>
> Second, I used to work for an Astronomer/Applied Optics Engineer, and
> was thus exposed, albeit superficially, to physical derivations of
> empirical optical particle count distributions; I didn't learn enough to
> help you, but he probably could - if you're interested, I can forward
> you his email, or if your reticent about making a "cold" contact, I can
> forward your email to him to see if he thinks he can help.
>
> DG
>
> Gary Pajer wrote:
> > On 8/23/07, *David Goldsmith* <David.L.Goldsmith@noaa.gov
> > <mailto:David.L.Goldsmith@noaa.gov>> wrote:
> >
> >     Please educate me: what are a "skew" and "kurtotid"
> >     Gaussians?  (What I
> >     learned: Gaussians are - by definition - devoid of any
> >     higher-than-second moments; wouldn't (shouldn't) a "Gaussian" with
> >     higher-than-second moments be called something else entirely?)
> >
> >
> > Exactly.   So I could rephrase my question:  what is the name of the
> > distribution that is similar to a normal distribution, but has a
> > variable amount of skewness?   Or is such a distribution a special
> > case of one of the many distributions in scipy?
> >
> > I *think*  the pdf of a "skew normal"  should be proportional to
> > exp(-a*x**2 - b*x**3) but that comes from a quick google search.
> >
> > Better yet:  what I'm trying to do is simulate the spectrum of an
> > optical emitter that I have.  The spectrum is nearly normal, but it is
> > not symmetric.  I'm looking for a model distribution.  I started by
> > looking for something quick and dirty.   If "quick" doesn't happen, I
> > might actually have to figure out if there is already a
> > theoretically-expected distribution for my case.  But in the meantime,
> > quick and dirty still sounds good.
> >
> > That's the real question.
> >
> > thanks for helping me express what I want  :)
> > -gary
> >
> >
> >
> >     DG
> >
> >     Gary Pajer wrote:
> >     > Do any of the distributions in scipy.stats make a skew Gaussian?
> >     > Ditto,  a Gaussian with kurtosis?
> >     >
> >     > thanks,
> >     > -gary
> >     >
> >
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