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RE: st: invgammap
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
of interest to you). See also -gammafit- on SSC.
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.
> 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?
> Small correction:
> The distribution concerned here is the _gamma_ distribution.
> Its quantile function is obtained as here from the -invgammap()-
> 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.
> Yulia Marchenko, StataCorp
> > Carlo Lazzaro <email@example.com> 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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