The Extreme Value Type I distributions requires that the population of events (e.g., annnual maximum precipitation, annual peak discharge, etc.) is unbounded in the direction of the extreme value and that the frequency of increasingly large events falls of in an exponential manner. Distributions that have these properties include the normal, log-normal, exponential, and gamma distributions. Assuming the population of events is normally distributed, the probability density function for the Extreme Value Type I Distribution is given by (Gumbel, 1958)
where a is a scale parameter and b is the mode of the distribution. The Type 1 Extreme Value Distribution is sometimes referred to as the Gumbel Extreme Value Distribution, the Fisher-Tippet Type I Distribution, or the Double Exponential Distribution.
The Extreme Value Type I distribution is often used to determine return periods of extreme events such as annual maximum rainfall or wind speed (Gumbel, 1954). In the United Kingdom it is used extensively for calculating flood recurrence (Cunnane, 1988).