Re: [R] new dgamma rate argument

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From: Peter Dalgaard BSA (p.dalgaard@biostat.ku.dk)
Date: Sat 12 Jan 2002 - 02:50:37 EST 

Message-id: <x21ygwnaya.fsf@blueberry.kubism.ku.dk>

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

> > 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

Are you sure? The *marginal* rate, i.e. the probability of observing
an event in [t,t+dt) should be independent of t, by stationarity. The
*conditional* rate given no event before time t is of course only a
constant in the (memoryless) Poisson process. 

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