Extreme Value Type I Distribution

The Extreme Value Type I distribution (also known as the Gumbel distribution) is used to calculate the frequency of maxima events when the distribution of all events (both big and small) is normally distributed.  Events will be normally distributed when they are the sum of a large number of independent random variables.  For example, if we assume that precipitation depth for any given storm is random, then the maxima of the total annual precipitation, being the sum of random events, should follow an Extreme Value Type I distribution.  In hydrologic applications, annual totals of such variables as precipitation and evaporation are often assumed to be the result of the sum of independent random events and thus tend to follow a normal distribution (Chow et al., 1988).  Thus this distribution is appropriate for calculating, e.g., the recurrence interval of large values of annual precipitation.  It is not, however, appropriate for calculating the recurrence interval of the annual maximum precipitation event.

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