查看“莱斯分布”的源代码

{{Link style|time=2015-12-12T05:12:26+00:00}}
{{noteTA
|1=zh-hans:分布; zh-hant:分佈;
|2=zh-hans:概率; zh-hant:機率;
|3=zh-hans:贝塞尔函数; zh-hant:貝索函數;
}}
{{機率分佈
|name       =Rice
|type       =density
|pdf_image  =[[File:Rice_distributiona_PDF.png|325px|Rice probability density functions σ=1.0]]<br /><small>Rice probability density functions for various ''v''   with σ=1.</small><br />[[File:Rice_distributionb_PDF.png|325px|Rice probability density functions σ=0.25]]<br /><small>Rice probability density functions for various ''v''   with σ=0.25.</small>
|cdf_image  =[[File:Rice_distributiona_CDF.png|325px|Rice cumulative density functions σ=1.0]]<br /><small>Rice cumulative density functions for various ''v''   with σ=1.</small><br />[[File:Rice_distributionb_CDF.png|325px|Rice cumulative density functions σ=0.25]]<br /><small>Rice cumulative density functions for various ''v''   with σ=0.25.</small>
|parameters =<math>v\ge 0\,</math><br /><math>\sigma\ge 0\,</math>
|support    =<math>x\in [0;\infty)</math>
|pdf        =<math>\frac{x}{\sigma^2}\exp\left(\frac{-(x^2+v^2)}
{2\sigma^2}\right)I_0\left(\frac{xv}{\sigma^2}\right)</math>
|cdf        =
|mean       =<math>\sigma  \sqrt{\pi/2}\,\,L_{1/2}(-v^2/2\sigma^2)</math>
|median     =
|mode       =
|variance   =<math>2\sigma^2+v^2-\frac{\pi\sigma^2}{2}L_{1/2}^2\left(\frac{-v^2}{2\sigma^2}\right)</math>
|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[[斯蒂芬·莱斯]]（[[:en:Stephen O. Rice]]）的名字命名，其[[概率密度函数]]为：
:<math>f(x|v,\sigma)=\,</math>
::<math>\frac{x}{\sigma^2}\exp\left(\frac{-(x^2+v^2)}
{2\sigma^2}\right)I_0\left(\frac{xv}{\sigma^2}\right)</math>
其中<math>I_0(z)</math>是修正的第一类零阶[[貝索函數]]（[[:en:Bessel function|Bessel function]]）。当<math>v=0</math>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])

:<math>\lim_{x\rightarrow -\infty}L_\nu(x)=\frac{|x|^\nu}{\Gamma(1+\nu)}</math>

It is seen that as <math>v</math> becomes large or <math>\sigma</math> becomes small the mean becomes <math>v</math> and the variance becomes <math>\sigma^2</math>

== 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
{{概率分布类型列表}}

[[Category:连续分布]]