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Estimation of the Parameters of Gumbel's Third Asymptotic Distribution by Different Methods
Author(s) -
Deininger Rolf A.,
Westfield James D.
Publication year - 1969
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr005i006p01238
Subject(s) - gumbel distribution , mathematics , fibonacci number , statistics , statistic , order statistic , least squares function approximation , estimation , distribution (mathematics) , extreme value theory , combinatorics , mathematical analysis , engineering , systems engineering , estimator
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.