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Simulation of probability distributions commonly used in hydrological frequency analysis
Author(s) -
Cheng KeSheng,
Chiang JieLun,
Hsu ChiehWei
Publication year - 2006
Publication title -
hydrological processes
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.222
H-Index - 161
eISSN - 1099-1085
pISSN - 0885-6087
DOI - 10.1002/hyp.6176
Subject(s) - cumulative distribution function , frequency distribution , frequency analysis , random variable , statistics , computer science , goodness of fit , probability distribution , normal distribution , probability density function , mathematics
Random variable simulation has been applied to many applications in hydrological modelling, flood risk analysis, environmental impact assessment, etc. However, computer codes for simulation of distributions commonly used in hydrological frequency analysis are not available in most software libraries. This paper presents a frequency‐factor‐based method for random number generation of five distributions (normal, log–normal, extreme‐value type I, Pearson type III and log‐Pearson type III) commonly used in hydrological frequency analysis. The proposed method is shown to produce random numbers of desired distributions through three means of validation: (1) graphical comparison of cumulative distribution functions (CDFs) and empirical CDFs derived from generated data; (2) properties of estimated parameters; (3) type I error of goodness‐of‐fit test. An advantage of the method is that it does not require CDF inversion, and frequency factors of the five commonly used distributions involves only the standard normal deviate. Copyright © 2006 John Wiley & Sons, Ltd.