莱斯分布

**Rice**
	概率密度函數; Rice probability density functions for various v with σ=1.; ; Rice probability density functions for various v with σ=0.25.
	累積分布函數; Rice cumulative density functions for various v with σ=1.; ; Rice cumulative density functions for various v with σ=0.25.
参数	;
值域
概率密度函数
期望值
方差
偏度	(complicated)
峰度	(complicated)

在概率论與数理統計领域，萊斯分布（Rice distribution或Rician distribution）是一種连续概率分布，以美国科学家斯蒂芬·莱斯（英语：Stephen O. Rice）的名字命名，其概率密度函数为：

f(x|v,\sigma )=\,

{\frac {x}{\sigma ^{2))}\exp \left({\frac {-(x^{2}+v^{2})}{2\sigma ^{2))}\right)I_{0}\left({\frac {xv}{\sigma ^{2))}\right)

其中 $I_{0}(z)$ 是修正的第一类零阶貝索函數（Bessel function）。当 $v=0$ 时，莱斯分布退化为瑞利分布。

矩

For large values of the argument, the Laguerre polynomial becomes (See Abramowitz and Stegun §13.5.1 （页面存档备份，存于互联网档案馆）)

\lim _{x\rightarrow -\infty }L_{\nu }(x)={\frac {|x|^{\nu )){\Gamma (1+\nu )))

It is seen that as $v$ becomes large or $\sigma$ becomes small the mean becomes $v$ and the variance becomes ${\displaystyle \sigma ^{2))$

Yongjun Xie and Yuguang Fang, "A General Statistical Channel Model for Mobile Satellite Systems" IEEE Transactions on Vehicular Technology, VOL. 49, NO. 3, MAY 2000. http://www.fang.ece.ufl.edu/mypaper/tvt00_xie.pdf （页面存档备份，存于互联网档案馆）

分类

概率密度函數 Rice probability density functions for various v with σ=1. Rice probability density functions for various v with σ=0.25.
累積分布函數 Rice cumulative density functions for various v with σ=1. Rice cumulative density functions for various v with σ=0.25.
参数	$v\geq 0\,$ $\sigma \geq 0\,$
值域	$x\in [0;\infty )$
概率密度函数	${\frac {x}{\sigma ^{2))}\exp \left({\frac {-(x^{2}+v^{2})}{2\sigma ^{2))}\right)I_{0}\left({\frac {xv}{\sigma ^{2))}\right)$
期望值	$\sigma {\sqrt {\pi /2))\,\,L_{1/2}(-v^{2}/2\sigma ^{2})$
方差	$2\sigma ^{2}+v^{2}-{\frac {\pi \sigma ^{2)){2))L_{1/2}^{2}\left({\frac {-v^{2)){2\sigma ^{2))}\right)$
偏度	(complicated)
峰度	(complicated)