LIKELIHOOD-BASED CONFIDENCE-INTERVALS FOR ESTIMATING FLOODS WITH GIVEN RETURN PERIODS

This paper discusses aspects of the calculation of likelihood-based co nfidence intervals for T-year floods, with particular reference to (1) the two-parameter gamma distribution; (2) the Gumbel distribution; (3 ) the two-parameter log-normal distribution, and other distributions r elated to the normal by Box-Cox transformations. Calculation of the co nfidence limits is straightforward using the Nelder-Mead algorithm wit h a constraint incorporated, although care is necessary to ensure conv ergence either of the Nelder-Mead algorithm, or of the Newton-Raphson calculation of maximum-likelihood estimates. Methods are illustrated u sing 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 giv en by use of the central limit theorem; for the same confidence probab ility, the confidence limits of the simulation were wider than those o f the central limit theorem, which failed more frequently to contain t he true quantile being estimated. The paper discusses possible applica tions of likelihood-based confidence intervals in other areas of hydro logical analysis.