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Fitting Johnson S B curve by the method of maximum likelihood to annual maximum daily rainfalls
Author(s) -
Kottegoda N. T.
Publication year - 1987
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/wr023i004p00728
Subject(s) - kurtosis , percentile , skewness , mathematics , log normal distribution , maximum likelihood , statistics , scale parameter , distribution (mathematics) , method of moments (probability theory) , scale (ratio) , gumbel distribution , mathematical analysis , extreme value theory , geography , cartography , estimator
A new method of fitting the Johnson S B distribution using maximum likelihood (ML) procedures is described. Commencing with assumed values for the location and scale parameters, estimates of all four parameters are found iteratively. This does not have the disadvantages of the method of moments for which estimates of the higher moments are required and the ambiguities of the method of percentiles in which estimates of parameters depend on the choice of percentiles. Application is made to sequences of annual maximum daily rainfalls in which the kurtosis is low when compared with that corresponding to the theoretical lognormal distribution for the observed skewness. In some cases the ML procedure is not feasible. Problems encountered with ML estimation and inadequacies arising from short samples on the choice of distribution are discussed.