[R] new dgamma rate argument

[Prof Brian Ripley]

On Fri, 11 Jan 2002, Martin Maechler wrote:

> >>>>> "Jim" == Jim Lindsey <james.lindsey at luc.ac.be> writes:
>
>     Jim> Can someone explain to me in what way the new
>     Jim> (dpqr)gamma parameter can be interpreted as a rate
>     Jim> (when shape != 1)? The only gamma rate that I am aware
>     Jim> of is the hazard rate given by dgamma/(1-pgamma), the
>     Jim> log of which is returned by my hgamma function (event
>     Jim> library).  Jim
>
> NEWS has
>
>     o	[dpqr]gamma now has third argument `rate' for S-compatibility
> 	(and for compatibility with exponentials).  Calls which use
> 	positional matching may need to be altered.
>
> i.e. one point of view (close to mine) could be:
>
>  The authors of R (R&R) called that argument of [dpqr]gamma()
>  `scale' as it should sensibly be called.
>  OTOH, (at least one of) the original S authors used `rate'
>  (for 1/scale) in a loose analogy with the exponential and
>  weibull distribution quite some time before R was born.  Now
>  that there is an increasing drive for S source compatibility
>  between the different S dialects --  whenever it's ``easy'' --
>  the compatible parametrization has been allowed as well.

I could add that this was precipated by finding two instances of people
porting S code and not noticing the difference in parameters, which is
somewhat dangerous and why the order was changed to be S compatible.

I see it is as a rate in the sense of an accelerated life model, just like
an exponential: the mean is proportional to 1/rate.

A quick poll of my bookshelf suggests that it is a common parametrization,
although Johnson & Kotz and the Encyclopedias of Statistical Science and
Biostatistics have the `shape' version, and also an offset (but I doubt
are independent authorities).

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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