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### Poisson distribution and Inter-Arrival Time problems

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```Hi,

I have a simulator where I generate inter-arrival times for different
events using a exponential distribution.

My problem is that I want to use Poisson distribution for arrivals,
and thus I want the inter-arrival times to reflect a poisson
distribution.

The problem is that I can only find the Poisson distribution defined
as
the number of events, or a count of events, during a given time and
average.

What should I do? The whole simulator is built around inter-arrival
times?

cheers,
Bosse

ps. For the exponential one, I use the inverse method on the CDF and
put a random value between 0.0 and 1.0 to get a random value that
follows the exponential distribution. ds.

```
 0

```"Bosse" <drbamdadi@hotmail.com> wrote in message
> Hi,
>
> I have a simulator where I generate inter-arrival times for different
> events using a exponential distribution.
>
> My problem is that I want to use Poisson distribution for arrivals,
> and thus I want the inter-arrival times to reflect a poisson
> distribution.
>
> The problem is that I can only find the Poisson distribution defined
> as the number of events, or a count of events, during a given time and
> average.
>

The exponential distribution and the Poisson distribution are the same:
If and only if interarrival times are exponentially distributed, the number
of events in a fixed timeslice are Poisson distributed. Accordingly, if
individual events are simulated, use the exponential distribution, if events
during a timeslice are simulated, use the Poisson distribution. Of course
the simulation of individual events shows more details.

--
Rommert J. Casimir
Room B725
Tilburg University
P.O. Box 90153
5000 LE Tilburg, The Netherlands
tel 3113 4662016 fax 3113 4663377
http://infolab.uvt.nl/people/casimir/BIKA/RC_HOME.HTM

This message was sent from home,
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Computing was more fun when nobody got rich from it

```
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7/24/2012 12:21:39 PM