# Statistics Gumbel Distribution – lesscss

By | October 1, 2019

# Statistics – Gumbel Distribution

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. ## Probability density function

Probability density function of Gumbel distribution is given as:

## Formula

\${ P(x) = frac{1}{beta} e^{[frac{x – alpha}{beta} –
e^{frac{x – alpha}{beta}}]} }\$

Where −

• \${alpha}\$ = location parameter.

• \${beta}\$ = scale parameter.

• \${x}\$ = random variable.

## Cumulative distribution function

Cumulative distribution function of Gumbel distribution is given
as:

## Formula

\${ D(x) = 1 – e^{-e^{frac{x – alpha}{beta}}}}\$

Where −

• \${alpha}\$ = location parameter.

• \${beta}\$ = scale parameter.

• \${x}\$ = random variable.

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