[R] new dgamma rate argument

[Jim Lindsey]

> 
>  
> > 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). 
> 
> Only a valid interpretation with k integer (the rate need not be
> one). But the rate of the resulting gamma process is still
> dgamma/(1-pgamma). Jim
> 
> > 
> > 
> > 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.

PS The rate per time unit of a stationary renewal process is only
constant and equal to 1/mean for a Poisson process i.e. exponential
interarrival times. Jim

> > 
> > -- 
> >    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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