# Distributions

### Gumbel Distribution

Used to model the extreme deviations from the median of distributions. Given the extreme(max/min) samples from an order statistic, models the distribution of these extreme values.

#### Model

= the location parameter

= the scale parameter

#### Mean

where , a.k.a Eulerâ€™s constant

#### Variance

#### Application

[1] Given the data for past 10 yearsâ€™ highest earthquake on richter scale, model

[2] TODO: The maximum value in a sample of RVs coming from exponential distribution can be modelled using Gumbel distribuion