[R] new dgamma rate argument

[Peter Dalgaard BSA]

Jim Lindsey <james.lindsey at luc.ac.be> writes:

> > 
> > 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
...
> Let me be clear. I am not arguing with the parametrization (although I
> prefer the glm one which is different again, and more in line with
> exponential families). I only dispute the name, "rate".
>   Jim

Don't kill me if I got the details wrong, but I think that if you
sample every k-th event of a Poisson process with rate 1 then the
interarrival time will be gamma(shape=k, rate=1). 


It would probably make better sense to have rate=1/k in that case, but
then there's the compatibility issue. In general, it would make sense
to have the rate defined as the events per time unit of a (stationary)
renewal process with a given interarrival distribution, alias 1/mean.

-- 
   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907
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