[SciPy-User] Mean arrivals per time unit -> Time between consecutive arrivals

josef.pktd@gmai... josef.pktd@gmai...
Fri Nov 27 08:58:18 CST 2009


On Fri, Nov 27, 2009 at 1:49 AM, Ram Rachum <cool-rr@cool-rr.com> wrote:
>  <josef.pktd <at> gmail.com> writes:
>> > YOu should take the interarrival time between two consecutive arrivals
>> > to be exponentially distributed with rate lambda, where lambda is the
>> > arrival rate. LIke this the number of arrivals in a fixed period is
>> > Poisson distributed. I never tried, but I suppose scipy contains a
>> > module to generate exponentially distributed rv's.
>>
>> The sum of iid exponential distributed rvs is gamma distributed
>> http://en.wikipedia.org/wiki/Gamma_distribution
>>
>> all available in scipy.stats
>>
>> Josef
>
> I don't understand. So you mean that the exponential thing would NOT be the
> right thing for the time between consecutive arrivals?

What I meant was that the distribution of the time to the next arrival
is exponential distributed. The time until you have k arrivals is the
sum of k exponentially distributed random variables and is gamma
distributed.

For simulation of queuing models http://pypi.python.org/pypi/SimPy
looks also useful, although I never used it.

Josef

>
> Also, why doesn't scipy automatically gives me the time between consecutive
> arrivals when I give the mean number of arrivals per time period?
>
> Ram.
>
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