Simulation of probability distributions commonly used in hydrological frequency analysis

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 comparsion 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 live commonly used distributions involves only the standard normal deviate. Copyright (c) 2006 John Wiley & Sons, Ltd.