# RE: st: invgammap

 From "Nick Cox" To "Carlo Lazzaro" , Subject RE: st: invgammap Date Tue, 8 May 2007 17:12:43 +0100

```Yulia's slip consists only of including the word
"inverse" in her first sentence. Delete it and all is fine.

Her code is just what I would have recommended
had she not replied first. Examples can be found embedded
in -qgamma- and -pgamma- on SSC (which may be

As was mentioned some months ago, I have various
routines for fitting and plotting the inverse gamma,
but they are not yet in the public domain.

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

Carlo Lazzaro

> Dear Yulia & Nick,
>
> thanks a lot for Your Kind hints and for Your time.
>
> PS Please, may I Kindly ask You to explain what does Yulia's
> slip mean?

Nick Cox

> 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
>
> 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
>
> > 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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```