[SciPy-user] skew Gaussian distribution

David Goldsmith David.L.Goldsmith@noaa....
Thu Aug 23 13:21:16 CDT 2007


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, 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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