Statistics 简明教程

Statistics - Beta Distribution

Beta 分布表示连续概率分布，该分布由两个正形状参数化，$ \alpha $ 和 $ \beta $，这两个正形状参数作为随机变量 x 的指数出现，并控制分布的形状。

The beta distribution represents continuous probability distribution parametrized by two positive shape parameters, $ \alpha $ and $ \beta $, which appear as exponents of the random variable x and control the shape of the distribution.

beta distribution

Probability density function

Beta 分布的概率密度函数给出如下：

Probability density function of Beta distribution is given as:

Formula

其中——

Where −

  1. ${ \alpha, \beta }$ = shape parameters.

  2. ${a, b}$ = upper and lower bounds.

  3. ${B(\alpha,\beta)}$ = Beta function.

Standard Beta Distribution

如果上限和下限为 1 和 0，则 Beta 分布称为标准 Beta 分布。它由以下公式驱动：

In case of having upper and lower bounds as 1 and 0, beta distribution is called the standard beta distribution. It is driven by following formula:

Formula

Cumulative distribution function

Beta 分布的累积分布函数给出如下：

Cumulative distribution function of Beta distribution is given as:

Formula

其中——

Where −

  1. ${ \alpha, \beta }$ = shape parameters.

  2. ${a, b}$ = upper and lower bounds.

  3. ${B(\alpha,\beta)}$ = Beta function.

它也被称为不完全 beta 函数比。

It is also called incomplete beta function ratio.