R help - Mar 2010 - Gamma parametrization

Dear R users,

?rgamma gives me :

               rgamma(n, shape, rate = 1, scale = 1/rate)

               rate: an alternative way to specify the scale.

               The Gamma distribution with parameters ‘shape’ = a and
               ‘scale’ = s has density
               f(x)= 1/(s^a Gamma(a)) x^(a-1) e^-(x/s)

Should I understand that scale=1/rate ? Is it written somewhere ?

Then rgamma(n, shape=a, scale = s) should be equivalent to rgamma(n,
shape=a, rate =1/s).

I don't find this very clear.

Thanks for your help.

Randall

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Dear Randall,

On Fri, Mar 19, 2010 at 10:24 AM, Randall Wrong <randall.wrong at
gmail.com> wrote:
> Dear R users,
>
> ?rgamma gives me :
>
> ? ? ? ? ? ? ? rgamma(n, shape, rate = 1, scale = 1/rate)
>
> ? ? ? ? ? ? ? rate: an alternative way to specify the scale.
>
> ? ? ? ? ? ? ? The Gamma distribution with parameters ?shape? = a and
> ? ? ? ? ? ? ? ?scale? = s has density
> ? ? ? ? ? ? ? f(x)= 1/(s^a Gamma(a)) x^(a-1) e^-(x/s)
>
> Should I understand that scale=1/rate ? Is it written somewhere ?
You are kidding, right?  It is written 8 lines above your question, by
my count.  :-)

Perhaps you meant rate = 1/scale.
>
> Then rgamma(n, shape=a, scale = s) should be equivalent to rgamma(n,
> shape=a, rate =1/s).
Yep:
dgamma(2, shape = 3, scale = 4)
dgamma(2, shape = 3, rate = 1/4)
>
> I don't find this very clear.
>
> Thanks for your help.
>
> Randall
>
The point is that some books (and software) parameterize by the
'scale', and a whole other bunch parameterize by the 'rate'. 
The
reader (and user) always needs to be careful that the version used is
the one expected. And the help file says that S doesn't have a
'scale'
parameter at all.

Just be careful, and you should be fine.  And IMHO, given that the PDF
of the density is shown it is reasonably clear as-is.

Best,
Jay





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