Can someone explain to me in what way the new (dpqr)gamma parameter can be interpreted as a rate (when shape != 1)? The only gamma rate that I am aware of is the hazard rate given by dgamma/(1-pgamma), the log of which is returned by my hgamma function (event library). Jim -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- 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 at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
>>>>> "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 NEWS has o [dpqr]gamma now has third argument `rate' for S-compatibility (and for compatibility with exponentials). Calls which use positional matching may need to be altered. i.e. one point of view (close to mine) could be: The authors of R (R&R) called that argument of [dpqr]gamma() `scale' as it should sensibly be called. OTOH, (at least one of) the original S authors used `rate' (for 1/scale) in a loose analogy with the exponential and weibull distribution quite some time before R was born. Now that there is an increasing drive for S source compatibility between the different S dialects -- whenever it's ``easy'' -- the compatible parametrization has been allowed as well. Martin -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- 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 at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
> > 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 -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- 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 at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._