Gumbel- (Lower) Distribution
The Gumbel- (Lower) distribution is an extreme minimum value distribution. This distribution is related to the Weibull family of distributions. In relation to the six separate extreme value distributions identified by Gumbel, the Gumbel- (Lower) distribution is a Type I lower extreme value, while the Weibull distribution is a Type III (Lower) distribution.
Calculations
The probability density function, f(t), and the survival function, that is reliability, 
, with respect to time t, follows for computing Gumbel- (Lower) distributions.
, with respect to time t, follows for computing Gumbel- (Lower) distributions.
Where:
In this case, δ and ξ are the scale and location parameters of the distribution. If a location parameter is used, see Location Parameter for additional calculation information.