Statistics 简明教程

Statistics - Rayleigh Distribution

瑞利分布是一个连续概率密度函数的分布。它以英国瑞利勋爵的名字命名。此分布广泛用于以下目的：

The Rayleigh distribution is a distribution of continuous probability density function. It is named after the English Lord Rayleigh. This distribution is widely used for the following:

  1. Communications - to model multiple paths of densely scattered signals while reaching a receiver.

  2. Physical Sciences - to model wind speed, wave heights, sound or light radiation.

  3. Engineering - to check the lifetime of an object depending upon its age.

  4. Medical Imaging - to model noise variance in magnetic resonance imaging.

rayleigh distribution

瑞利分布的概率密度函数定义为：

The probability density function Rayleigh distribution is defined as:

Formula

其中——

Where −

  1. ${\sigma}$ = scale parameter of the distribution.

累积分布函数瑞利分布的定义为：

The comulative distribution function Rayleigh distribution is defined as:

Formula

其中——

Where −

  1. ${\sigma}$ = scale parameter of the distribution.

Variance and Expected Value

瑞利分布的期望值或均值表示为：

The expected value or the mean of a Rayleigh distribution is given by:

瑞利分布的方差由以下公式得出：

The variance of a Rayleigh distribution is given by: