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Use of censored data in the estimation of Gumbel distribution parameters for annual maximum flood series
Author(s) -
Leese Morven N.
Publication year - 1973
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/wr009i006p01534
Subject(s) - gumbel distribution , statistics , maximum likelihood , sample (material) , series (stratigraphy) , mathematics , flood myth , estimation , data set , distribution (mathematics) , econometrics , extreme value theory , geography , engineering , geology , physics , mathematical analysis , paleontology , archaeology , systems engineering , thermodynamics
Maximum likelihood equations for the estimation of Gumbel distribution parameters from censored samples are derived; expressions for their large‐sample standard errors are also given. Censored samples arising in annual maximum flood series are described, and it is shown that a set of historic floodmarks may, under certain assumptions, be combined with recent noncensored data, to form what is essentially a censored sample. Maximum likelihood methods are applied to such a sample, and the resulting estimates are compared with those obtained from the recent data alone. The estimates agree closely, and the use of the extra information contained in the historic floodmarks is shown to lead to a reduction in the large‐sample standard errors of the estimates.