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R: st: invgammap


From   "Carlo Lazzaro" <carlo.lazzaro@tin.it>
To   <statalist@hsphsun2.harvard.edu>
Subject   R: st: invgammap
Date   Tue, 8 May 2007 18:05:57 +0200

Dear Yulia & Nick,

thanks a lot for Your Kind hints and for Your time.

Kind Regards,

Carlo

PS Please, may I Kindly ask You to explain what does Yulia's slip mean?

Thanks a lot again,

Carlo
-----Messaggio originale-----
Da: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di Nick Cox
Inviato: marted́ 8 maggio 2007 17.26
A: statalist@hsphsun2.harvard.edu
Oggetto: RE: st: invgammap

Small correction: 

The distribution concerned here is the _gamma_ distribution. 

Its quantile function is obtained as here from the -invgammap()-
function. 

There is another distribution, the inverse gamma, which 
is distinct. It is also known as the reciprocal gamma, Vinci
or Pearson Type V distribution. 

Yulia's slip arises because the word "inverse" is 
overloaded. 

In one sense, "inverse" has the sense of
"inverse function". This is the case with the quantile function
which is, the inverse of the (cumulative) distribution function. 
The prefix "inv" in -invgammap()- is there for this reason. 

In another sense, "inverse" has the sense of "reciprocal". 
Thus, the inverse gamma is so-called because (for example)
y is distributed as an inverse gamma if 1/y is distributed 
as a gamma. 

Nick 
n.j.cox@durham.ac.uk 

Yulia Marchenko, StataCorp
 
> Carlo Lazzaro <carlo.lazzaro@tin.it> asks about the scale 
> parameter of the
> inverse Gamma distribution:
> 
> > performing an invgammap with random probabilities
> >
> > generate alfa=invgammap(a,uniform())
> >
> > I have noticed the absence of the beta parameter of the 
> gamma distributions.
> > May this absence affect the results of the probabilistic 
> invgammap function?
> 
> Although probability functions -gammap()- and -invgammap()- 
> do not allow
> specifying the scale parameter, Carlos can obtain the 
> probabilities of the
> Gamma distribution with shape parameter a and scale parameter 
> beta as follows.
> 
>  . generate gamma = gammap(a, x/beta)
> 
> To obtain the inverse of the Gamma distribution with shape 
> parameter a and
> scale parameter beta, Carlos can use
> 
>  . generate x = beta*invgammap(a, gamma)
> 
> or, using his example,
> 
>  . generate alfa = beta*invgammap(a,uniform())

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