莱斯分布

{{機率分佈
|name =Rice
|type =density
|pdf_image =
Rice probability density functions for various v   with σ=1.

Rice probability density functions for various v   with σ=0.25.
|cdf_image =
Rice cumulative density functions for various v   with σ=1.

Rice cumulative density functions for various v   with σ=0.25.
|parameters =v\ge 0\,
\sigma\ge 0\,
|support =x\in [0;\infty)
|pdf =\frac{x}{\sigma^2}\exp\left(\frac{-(x^2+v^2)}
{2\sigma^2}\right)I_0\left(\frac{xv}{\sigma^2}\right)
|cdf =
|mean =\sigma \sqrt{\pi/2}\,\,L_{1/2}(-v^2/2\sigma^2)
|median =
|mode =
|variance =2\sigma^2+v^2-\frac{\pi\sigma^2}{2}L_{1/2}^2\left(\frac{-v^2}{2\sigma^2}\right)
|skewness =(complicated)
|kurtosis =(complicated)
|entropy =
|mgf =
|char =
}}

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
极限情况
For large values of the argument, the Laguerre polynomial becomes
(See Abramowitz and Stegun [http://www.math.sfu.ca/~cbm/aands/page_508.htm §13.5.1] )

:\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 \sigma^2

相關條目

• Stephen O. Rice (1907-1986)
• 瑞利分布
• 莱斯衰落

外部連結

• 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