Author(s): Fahim Ashkar; Taha B. M. J. Ouarda; Bernard Bobee
Linked Author(s):
Keywords: Hydrology; Floods; Frequency analysis; Confidence intervals; Quantiles; Sm all samples
Abstract: In engineering activities such as the design of a flood-control structure or the estimation of flood damage, decisions are often made based on a sample x_1, …x_n of flood values (maximum annual flood discharges, for example), which is often of small size. It is common practice to use a statistical distribution, or "model", f (x) =f (x; θ_1, …, θ_k), with parameters θ_1, …, θ_k, to fit the sample values, and to use this model to estimate an extreme flood event x_p, corresponding to a small probability of exceedance 1-p, or return period T=1/ (1-p). The unknown parameters θ_i; i=1, …, k of the model, are estimated from the sample and then used to estimate x_p, so the precision of this estimation depends on the accuracy with which the θ_i's have been obtained. This precision can be assessed by constructing confidence intervals (CI's) for x_p. Sometimes, simple but relatively inaccurate methods for calculating CI's for x_p have been used, although more accurate small-sample techniques might be available. Most of the small-sample techniques that have been developed in the literature, have been based on the method of maximum likelihood for parameter estimation. We review some of these small-sample methods for a number of distributions, including the normal/lognormal, Pearson Type Ⅲ/log-Pearson Type Ⅲ, Weibull/Gumbel, and exponential/Pareto.
Year: 1993