Gumbel Distribution

Tags: #Math #Statistics

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}}
                            

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 Miller
    Hoping to get over the hurdle of this exam.
    2023-12-18 00:00

    Reply


    Mildred Turner reply to Richard Miller
    Gooood Luck, Man!
    2023-12-28 00:00:00.0

    Reply


  • Betty Taylor
    The anxiety of this exam is overwhelming; I hope I pass.
    2023-08-02 00:00

    Reply


    Timothy Cook reply to Betty Taylor
    Best Wishes.
    2023-08-30 00:00:00.0

    Reply


  • Jason Hall
    A pass on this exam would mean the world to me.
    2023-09-01 00:00

    Reply


    Clarence Briggs reply to Jason Hall
    Best Wishes.
    2023-09-14 00:00:00.0

    Reply