Application of profile likelihood function.pdf

SCIENCE CHINA Technological Sciences ? Science China Press and Springer-Verlag Berlin Heidelberg 2013 *Corresponding author (email: yandh@) December 2013 Vol.56 No.12: 3151–3160 doi: 10.1007/s11431-013-5421-0 Application of profile likelihood function to the uncertainty analysis of hydrometeorological extreme inference LU Fan, WANG Hao, YAN DengHua*, ZHANG DongDong XIAO WeiHua State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China Received June 13, 2013; accepted November 5, 2013; published online November 22, 2013 Profile likelihood function is introduced to analyze the uncertainty of hydrometeorological extreme inference and the theory of estimating confidence intervals of the key parameters and quantiles of extreme value distribution by profile likelihood function is described. GEV (generalized extreme value) distribution and GP (generalized Pareto) distribution are used respectively to fit the annual maximum daily flood discharge sample of the Yichang station in the Yangtze River and the daily rainfall sample in 10 big cities including Guangzhou. The parameters of the models are estimated by maximum likelihood method and the fitting results are tested by probability plot, quantile plot, return level plot and density plot. The return levels and confidence intervals of flood and rainstorm in different return periods are calculated by profile likelihood function. The results show that the asymmetry of the profile likelihood function curve increases with the return period, which can reflect the effect of the length of sample series and return periods on confidence interval. As an effective tool for estimating confidence interval of the key pa- rameters and quantiles of extreme value distribution, profile likelihood function can lead to a more accurate result and help to analyze the uncertainty of e