[R] new dgamma rate argument

[Peter Dalgaard BSA]

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

> > 
> > Jim Lindsey <james.lindsey at 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. 
> 
> Yes this is a weird property of these things. Stationarity of times
> between events does not carry over to stationarity of frequency of
> events in small intervals. See for example, Cox and Lewis, p.61.

And vice versa. A "stationary renewal process" is one that is
stochastically delayed to make the *second* property hold and the
delay distribution is different from that of the interarrival time.
Otherwise it wouldn't be a stationary process.

-- 
   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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