Type-1 Gumbel distribution
Encyclopedia
In probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...

, the Type-1 Gumbel density function is


for


The distribution is mainly used in the analysis of extreme values and in survival analysis
Survival analysis
Survival analysis is a branch of statistics which deals with death in biological organisms and failure in mechanical systems. This topic is called reliability theory or reliability analysis in engineering, and duration analysis or duration modeling in economics or sociology...

(also known as duration analysis or event-history modelling).
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