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• ## URL for generating functions ?

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• Hello, I need a URL containing a list of discrete Probability distributions with the corresponding probability generating functions. Something like that :
Message 1 of 3 , Jun 9, 2005
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Hello,

I need a URL containing a list of discrete Probability distributions
with the corresponding probability generating functions.
Something like that :
Poisson P(X=n)=a^n/n!*exp(-a), n>=0 E(t^X)=exp(a(t-1))
geometrical P(X=n)=p(1-p)^(n-1), n>=1 E(t^X)=tp/(1-t-tp)
and so on, for as many distributions as possible
(binomial, negative binomial, uniform, hypergeometrical, Zipf, etc)
I need it in a very compact, easy-to-read for non-probabilists,
form.
I tried google, but "probability" generating" and "function" are
very frequent words appearing in various contexts, some of them
irrelevant, other ones containing a single generating function
lost in a bunch of mathematical informations...
Does such a URL exist ? Where ?

Myriam
• ... Hi Myriam, I really thought I had the answer to this:-( There is a pretty good list called a compendium of common probability distributions on the
Message 1 of 3 , Jun 9, 2005
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> I need a URL containing a list of discrete Probability distributions
> with the corresponding probability generating functions.

Hi Myriam,

I really thought I had the answer to this:-( There is a pretty
good list called "a compendium of common probability distributions"
on the following page:

http://www.geocities.com/~mikemclaughlin/math_stat/Dists/Compendium.html

Unfortunately, there seems to be no information about characteristic
functions (or moment generating functions). So I'll keep looking.

Noel.
• Hi Noel, Thanks for your answer, the link is really interesting, especially the characterization given for each distribution. But the generating functions
Message 1 of 3 , Jun 10, 2005
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Hi Noel,

the "characterization" given for each distribution.
But the generating functions are not given :-(
Perhaps the URL I'm looking for doesn't exist...

Thanks again and do not invest too much time in this. I thought
perhaps someone here already knows of such an URL and it will
save me time. But if it is necessary to collect the generating
functions from different locations, I can do it.

Myriam

--- In probability@yahoogroups.com, "Noel Vaillant" <vaillant@p...> wrote:
> > I need a URL containing a list of discrete Probability distributions
> > with the corresponding probability generating functions.

>http://www.geocities.com/~mikemclaughlin/math_stat/Dists/Compendium.html
>
> Unfortunately, there seems to be no information about characteristic
> functions (or moment generating functions). So I'll keep looking.
>
> Noel.
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