Effect of tail behavior assumptions on flood predictions

Two of the distributions most widely used in flood magnitude modeling are the Gumbel type 1 extreme‐value distribution and the log Pearson type 3. These represent two fundamentally different assumptions about distribution tail behavior in that extreme events from the log Pearson type 3 distribution follow the Gumbel type 2 extremal distribution. This paper compares these two assumptions by comparing flood predictions by the type 1 and type 2 models. For the Gumbel type 1 distribution the ratio of x n 1 the magnitude of a flood with a return period n 1 , to x n 2 , the magnitude for a shorter return period n 2 , can be estimated by an upper bound which is In n 1 /ln n 2 . It is shown that the ratio of x n 1 / x n 2 from the type 2 distribution is always greater than that from the type 1, approximated by ( n 1 / n 2 ) 1/ k . An analysis of flow data collected in the United States indicates that in the majority of cases the best fitting type 2 distribution does not have a finite variance and often not even a finite mean. The impact of this on statistical data analysis is discussed.