Gumbel Distribution
Tags: #Math #StatisticsEquation
$$x \sim \text{Gumbel}(\mu,\beta), \\ \frac{1}{\beta} e^{-(z + e^{-z})}, z=\frac{x - \mu}{\beta}, \\ e^{-e^{-(x-\mu)/\beta}}$$Latex Code
x \sim \text{Gumbel}(\mu,\beta), \\
\frac{1}{\beta} e^{-(z + e^{-z})}, z=\frac{x - \mu}{\beta}, \\
e^{-e^{-(x-\mu)/\beta}}
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Introduction
Equation
$$x \sim \text{Gumbel}(\mu,\beta)$$ $$\frac{1}{\beta} e^{-(z + e^{-z})}, z=\frac{x - \mu}{\beta}$$ $$e^{-e^{-(x-\mu)/\beta}}$$
Latex Code
x \sim \text{Gumbel}(\mu,\beta), \\
\frac{1}{\beta} e^{-(z + e^{-z})}, z=\frac{x - \mu}{\beta}, \\
e^{-e^{-(x-\mu)/\beta}}
Explanation
Latex code for the Gumbel Distribution. The Gumbel Distribution is used to model the distribution of the maximum of a number of samples of various distributions.
- PDF of Gumbel distribution: $$\frac{1}{\beta} e^{-(z + e^{-z})}, z=\frac{x - \mu}{\beta}$$
- CDF of Gumbel distribution: $$e^{-e^{-(x-\mu)/\beta}}$$
- Mean value of Gumbel distribution: $$\mu +\beta\gamma$$
- Variance value of Gumbel distribution: $$\frac{\pi^{2}}{6}\beta^{2}$$
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