From: Peter Dalgaard BSA (p.dalgaard@biostat.ku.dk)
Date: Mon 14 Jan 2002 - 20:28:46 EST
Message-id: <x2sn99p9gx.fsf@blueberry.kubism.ku.dk>
Jim Lindsey <james.lindsey@luc.ac.be> writes:
> >
> > 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.
>
> 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@biostat.ku.dk) FAX: (+45) 35327907 -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request@stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
This archive was generated by hypermail 2.1.3 : Thu 17 Jan 2002 - 11:10:11 EST