A comparison of parametric and nonparametric methods for low-flow frequency analysis

With the increased reporting of extreme events and their associated economic and social impacts, it is critical that our methodology or approaches to estimating their probability of occurrence be reliable. A number of probability distributions have been found to be applicable to low-now frequency analysis, though the log-Pearson Type III (LP3) and Weibull distributions are perhaps most often used in practical applications. Such methods are referred to as ''parametric methods''. Often, however, the above distributions may give lower drought bounds that are larger than the smallest observations, particularly when the method of moments is used to estimate the parameters. Such estimates are unsatisfactory. Some controversy also exists when the lower boundary of a theoretical distribution assumes negative or seemingly arbitrary values. In such cases, some have found it preferable to set the location parameter to zero, and thereby fit the two parameter form of the distribution. In addition, there are other theoretical and practical problems using the above distributions, especially when the data are multimodal or contain zeros. In order to overcome some of the problems inherent in parametric methods, an alternative approach that is referred to in the literature as a ''nonparametric method'' can be adapted to low-flow frequency analysis. This article describes the nonparametric method and shows that it has some theoretical and practical advantages over its parametric counterpart. The Weibull distribution and the nonparametric method are compared using Monte Carlo procedures. Results show that the nonparametric method can overcome the lower boundary disadvantages of the parametric methods, are robust, and are particularly easy to apply. As well, it is found from this simulation study that the nonparametric method is as accurate as parametric procedures, in this case the Weibull distribution, for estimating drought quantiles.