Type-I Extreme Value Distribution

The type-I extreme value (a.k.a. Gumbel) distribution is used to model the distribution of a maximum (or minimum) value of a number of samples of various distributions.
It is case one of the generalized extreme value distribution (the others being type-II/Frechet, and type-III/Weibull).
Been seeing this a lot in models as the distribution for the error term, because it gives a nice expression for the probability of a particular alternative. More precisely: in the latent variable formulation of the multinomial logit model—common in discrete choice models—the errors of the latent variables follow a type-I EV distribution. This is useful because the difference of two type-I EV distributed RVs has a logistic distribution.
In the latent variable formulation of the multinomial logit model — common in discrete choice theory — the errors of the latent variables follow a Gumbel distribution. This is useful because the difference of two Gumbel-distributed random variables has a logistic distribution.