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## Re: [Help-gsl] Understand how to use the Gumbel Type 1 distribution

 From: Matias Berrueta Subject: Re: [Help-gsl] Understand how to use the Gumbel Type 1 distribution Date: Thu, 08 Mar 2018 09:20:53 +0000

```Awesome, man thanks a LOT!

On Thu, Mar 8, 2018 at 12:14 AM Martin Jansche <address@hidden> wrote:

> Per the GSL manual [
> https://www.gnu.org/software/gsl/manual/html_node/The-Type_002d1-Gumbel-Distribution.html]
> we have
>
> p(x) dx = a b \exp(-(b \exp(-ax) + ax)) dx
>
> And Wikipedia has
>
> p(x) = 1/beta exp(-(z + exp(-z)))  where  z = (x - mu)/beta
>
> Now substitute a = 1/beta and write z= ax - mu/beta
>
> p(x) = a exp(-(ax - mu/beta + exp(-ax + mu/beta))
>
> And so
>
> p(x) = a exp(mu/beta) exp(-(ax + exp(-ax) exp(mu/beta))
>
> This matches the GSL definition when you substitute b = exp(mu/beta).
>
> tl;dr:  a = 1.0/beta; b = exp(mu/beta);
>
> On Sat, Mar 3, 2018 at 2:10 PM, Matias Berrueta <address@hidden>
> wrote:
>
>> Hello there,
>>
>> Sorry to bother you guys, but I'm trying to use the
>>
> * `double gsl_ran_gumbel1(const gsl_rng * r, double a, double b)`*
>
>
>> without success.
>>
>> I have the `location` & `scale` parameters (
>> https://en.wikipedia.org/wiki/Gumbel_distribution)
>> how to convert those to `a` & `b` ?
>>