Likelihood-based confidence intervals for estimating floods with given return periods

Abstract

This paper discusses aspects of the calculation of likelihood-based confidence intervals for T-year floods, with particular reference to (I) the two-parameter gamma distribution; (2) the Gumbel distri- bution; (3) the two-parameter log-normal distribution, and other distributions related to the normal by Box Cox transformations. Calculation of the confidence limits is straightforward using the Nelder Mead algorithm with a constraint incorporated, although care is necessary to ensure convergence either of the Nelder-Mead algorithm, or of the Newton-Raphson calculation of maximum-likelihood estimates. Methods are illustrated using records from 18 gauging stations in the basin of the River Itajai-Acu, State of Santa Catarina, southern Brazil. A small and restricted simulation compared likelihood-based confidence limits with those given by use of the central limit theorem; for the same confidence probability, the confidence limits of the simulation were wider than those of the central limit theorem, which failed more frequently to contain the true quantile being estimated. The paper discusses possible applications of like- lihood-based confidence intervals in other areas of hydrological analysis