[R] new dgamma rate argument

[Jim Lindsey]

> 
> 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.
  Jim
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