Statistics 简明教程

Statistics - Gumbel Distribution

Gumbel 分布表示各种分布中所用样本的最大值或最小值的极值分布。它用于对峰值的分布建模。例如,要显示一年的峰值温度分布,如果存在 10 年内的最高温度列表。

Gumbel Distribution represents the distribution of extreme values either maximum or minimum of samples used in various distributions. It is used to model distribution of peak levels. For example, to show the distribution of peak temperatures of the year if there is a list of maximum temperatures of 10 years.

\statistics\images\gumbel distribution

Probability density function

Gumbel 分布的概率密度函数表示为:

Probability density function of Gumbel distribution is given as:

Formula

其中——

Where −

  1. ${\alpha}$ = location parameter.

  2. ${\beta}$ = scale parameter.

  3. ${x}$ = random variable.

Cumulative distribution function

Gumbel 分布的累积分布函数表示为:

Cumulative distribution function of Gumbel distribution is given as:

Formula

其中——

Where −

  1. ${\alpha}$ = location parameter.

  2. ${\beta}$ = scale parameter.

  3. ${x}$ = random variable.