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Properties of the three‐parameter log normal probability distribution
Author(s) -
Burges Stephen J.,
Lettenmaier Dennis P.,
Bates Courtney L.
Publication year - 1975
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/wr011i002p00229
Subject(s) - estimator , mathematics , standard deviation , skew , statistics , skew normal distribution , probability distribution , estimation theory , distribution (mathematics) , location parameter , normal distribution , mathematical analysis , computer science , telecommunications
Mathematical properties of the three‐parameter log normal probability distribution are detailed. Two methods for estimation of the third parameter a are compared. The estimator of a using sample mean, median, and standard deviation is found to be more variable and have larger bias for distributions of interest in operational hydrology than the estimator using sample mean, standard deviation, and skew. Graphical solutions for the third parameter a are presented; a single feasible value of a is shown to result when the skew estimator is used; two feasible solutions result when the median estimator is used. The smaller of the two solutions is shown to correspond to skews of less than 5.87 and hence is the desired solution in most hydrologic applications.