# How does addition of a constant affect a Gumbel random variable

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?

• 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. – mathuser001 Jun 30 at 4:24
• $\mu$ 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 $(c+\mu,\sigma)$ ? – Raskolnikov Jun 30 at 6:13