Poisson point process: Difference between revisions

Revision as of 12:51, 6 December 2022

Revision as of 13:20, 6 December 2022

Line 23:

:<math> \Pr \{N=n\}=\frac{\Lambda^n}{n!} e^{-\Lambda} </math>

where <math display=inline> n!</math> denotes <math display=inline> 分歧分期n</math> [[factorial]] and the parameter <math display=inline> \Lambda</math> determines the shape of the distribution. (In fact, <math display=inline> \Lambda</math> equals the expected value of <math display=inline> N</math>.)

By definition, a Poisson point process has the property that the number of points in a bounded region of the process's underlying space is a Poisson-distributed random variable.<ref name="Kingman1992page11">{{cite book|author=J. F. C. Kingman|title=Poisson Processes|url=https://books.google.com/books?id=VEiM-OtwDHkC|date=17 December 1992|publisher=Clarendon Press|isbn=978-0-19-159124-2|pages=11–12}}</ref>