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Exact distribution of the peak streamflow
Author(s) -
Nadarajah Saralees
Publication year - 2007
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 - 10.1029/2006wr005300
Subject(s) - streamflow , weibull distribution , probability density function , mathematics , percentile , distribution (mathematics) , function (biology) , moment (physics) , probability distribution , cumulative distribution function , moment generating function , statistics , physics , geography , mathematical analysis , cartography , drainage basin , evolutionary biology , biology , classical mechanics
Iacobellis and Fiorentino (2000) and Fiorentino et al. (2006) proposed modeling the peak of direct streamflow as a product of two independent random variables: one gamma distributed and the other Weibull distributed. However, the papers did not provide any results on the theoretical probability distribution of the peak streamflow. In this note, we derive explicit expressions for the probability density function, cumulative distribution function, and the moment measures of the peak streamflow. We also show how one could determine the percentiles of the peak streamflow. The results of this note could be applied more widely than just for the modeling of peak streamflow.