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}}
Have Fun
Let's Vote for the Most Difficult Equation!
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: $$\frac{\pi^{2}}{6}\beta^{2}$$
Related Documents
Related Videos
Discussion
Comment to Make Wishes Come True
Leave your wishes (e.g. Passing Exams) in the comments and earn as many upvotes as possible to make your wishes come true
-
Richard MillerHoping to get over the hurdle of this exam.Mildred Turner reply to Richard MillerGooood Luck, Man!2023-12-28 00:00 -
Betty TaylorThe anxiety of this exam is overwhelming; I hope I pass.Timothy Cook reply to Betty TaylorBest Wishes.2023-08-30 00:00 -
Jason HallA pass on this exam would mean the world to me.Clarence Briggs reply to Jason HallBest Wishes.2023-09-14 00:00
Reply