## Quick Reference

The distribution of the distance between a point and its nearest neighbour in a spatial Poisson process. Also the distribution of the distance from the origin in *n*-dimensional space to the point (*X*_{1}, *X*_{2},…, *X** _{n}*), where

*X*

_{1},

*X*

_{2},…,

*X*

*are independent normal variables, each with expectation 0 and variance*

_{n}*σ*

^{2}. The probability density function f is given by where

*σ*>0 and Γ is the gamma function. The distribution has mean μ and variance

*v*given by The distribution has mode

*σ*√

*n*-1. In the case

*n*=2, the expressions for the mean and variance simplify to

*σ*√½

*π*and ½

*σ*

^{2}(4-

*π*) respectively.

**Rayleigh distribution.** The shape of the distribution depends on the value of the parameters *σ* and *n*. The figure illustrates the dependence on *n*, with *σ*=1.

*Subjects:*
Probability and Statistics.