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Using partial probability weighted moments to fit the extreme value distributions to censored samples
Author(s) -
Wang Q. J.
Publication year - 1996
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 - 10.1029/96wr00352
Subject(s) - gumbel distribution , censoring (clinical trials) , quantile , mathematics , extreme value theory , extrapolation , generalized extreme value distribution , statistics , interpolation (computer graphics) , monte carlo method , computer science , animation , computer graphics (images)
The estimation of floods of large return periods from lower bound censored samples may often be advantageous because interpolation and extrapolation are made by exploring the trend of larger floods in each of the records. The method of partial probability weighted moments (partial PWMs) is an useful technique for fitting distributions to censored samples. In this paper, partial PWMs are redefined along with a brief discussion on the definition of ordinary PWMs. The expression for partial PWMs is derived for the extreme value type I or Gumbel distribution. Combined with those for the extreme value type II and III distributions, an unified expression for partial PWMs is presented for the generalized extreme value (GEV) distribution. The equations for solving the distribution parameters are provided. Monte Carlo simulation shows that lower bound censoring at a moderate level does not unduly reduce the efficiency of high‐quantile estimation even if the samples have come from a true GEV distribution.