Re: simulating a Poisson Forest

*Subject*: [mg2889] Re: simulating a Poisson Forest*From*: jorma.virtamo at vtt.fi (Jorma Virtamo)*Date*: 4 Jan 1996 13:42:47 -0600*Approved*: usenet@wri.com*Distribution*: local*Newsgroups*: wri.mathgroup*Organization*: Wolfram Research, Inc.*Sender*: mj at wri.com

deb at Alceon.com (David E. Burmaster) wrote: >Dear MathGroupers > >Does anyone know a simple algorithm to simulate a "Poisson Forest" of >random points inside a rectangle in a plane? > >If each coordinate in the {x, y}-pairs is drawn from an independent Uniform >distribution, will that create a Poisson forest? > Yes, it does. If you have to create just one realization of the 2-dim Poisson process with intensity lambda, take the number of points N to be the closest integer to the mean m=lambda*A, where A is the area to be covered. If you have to create several realizations remember to draw N in each realization from the Poisson distribution with mean m. If m is a very large number it may not matter much whether you draw N from this distribution or whether you use the closest integer to the mean. But if m is not so large the difference can be important. -- Jorma Virtamo ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Jorma Virtamo VTT Information Technology phone: +358 0 456 5612 Telecommunications fax: +358 0 455 0115 P.O. Box 1202 email: jorma.virtamo at vtt.fi FIN-02044 VTT web: http://www.vtt.fi/tte/ Finland