Statistical Estimation Methods in Hydrological Engineering

In designing civil engineering structures use is made of probabilistic calculation methods. Stress and load parameters are described by statistical distribution functions. The parameters of these distribution functions can be estimated by various methods. An extensive comparison of these different estimation methods is given in this paper. The main point of interest is the behaviour of each method for predicting p-quantiles (the value which is exceeded by the random variable with probability p), where p«1. The estimation of extreme quantiles corresponding to a small probability of exceedance is commonly required in the risk analysis of hydraulic structures. Such extreme quantiles may represent design values of environmental loads (wind, waves, snow, earthquake), river discharges, and flood levels specified by design codes and regulations (TAW, 1990). In this paper the performance of the parameter estimation methods with respect to its small sample behaviour is analyzed with Monte Carlo simulations, added with mathematical proofs. In civil engineering practice many parameter estimation methods for probability distribution functions are in circulation. Well known methods are for example: the method of moments (Johan Bernoulli, 1667-1748), the method of maximum likelihood (Daniel Bernoulli, 1700-1782), the method of least squares (on the original or on the linearized data), (Gauss, 17771855), the method of Bayesian estimation (Bayes, 1763), the method of minimum cross entropy (Shannon, 1949), the method of probability weighted moments (Greenwood et al., 1979), the method of L-moments (Hosking, 1990). Textbooks, such as Benjamin and Cornell (1970), Berger (1980), treat the traditional methods in detail. The methods will be briefly reviewed in this paper.