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莱斯分布

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Rice
Rice probability density functions σ=1.0
Rice probability density functions for various v   with σ=1.
Rice probability density functions σ=0.25
Rice probability density functions for various v   with σ=0.25.
概率density函數
Rice cumulative density functions σ=1.0
Rice cumulative density functions for various v   with σ=1.
Rice cumulative density functions σ=0.25
Rice cumulative density functions for various v   with σ=0.25.
累積分佈函數
參數 v\ge 0\,
\sigma\ge 0\,
支撑集 x\in [0;\infty)
概率density函數 \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)

概率论数理統計领域,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:

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

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极限情况[编辑]

For large values of the argument, the Laguerre polynomial becomes (See Abramowitz and Stegun §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[编辑]

外部連結[编辑]