Description:
<jats:p>Estimation of the parameters of Gumbel's third asymptotic distribution of the smallest value has been accomplished in the past by the following methods: (1) the method of moments; (2) using an order statistic on the characteristic drought; and (3) using the smallest observed drought. These three methods are compared with a fourth method that uses sequential least squares and a Fibonacci search. Based on estimates of the parameters of 44 rivers in the United States, it appears that methods 1, 2, and 3 do not give a satisfactory estimate of the smallest drought in a large number of cases. The method of using an order statistic was the least successful. The use of the least squares and Fibonacci search approach gave more acceptable estimates than the other methods.</jats:p>