Suppose $X$ is a Gumbel (Type-1 extreme value) random variable with shape and scale parameters given by $(μ, σ)$. What is the distribution of $c+X$, where $c$ is a constant?

  • $\begingroup$ Why downvote? It's sad how some people always would think basic questions as a student's try to getting answers from internet. I am just curious and asking this in order to understand Gumbel Reparametrization trick. $\endgroup$ – mathuser001 Jun 30 at 4:24
  • $\begingroup$ $\mu$ is not a shape parameter but a location parameter, and in that case is there any reason to expect that $c+X$ will be anything else but Gumbel distributed with parameters $(c+\mu,\sigma)$ ? $\endgroup$ – Raskolnikov Jun 30 at 6:13

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