Uncertainty of quantile estimators using the population index flood method

Abstract

The population index flood (PIF) method is an analytical model that has been recently suggested for regional frequency analysis. In this paper, explicit equations based on Fisher's information are derived for estimating the standard error of at‐site quantile estimators for two regional PIF methods utilizing the generalized extreme value distribution with maximum likelihood estimation. These explicit equations are used to calculate the asymptotic gain in using regional frequency analysis as opposed to single site frequency analysis. Simulation experiments for different sized regions and different values of the shape parameter show that the suggested methods for estimating the standard error of at‐site quantile estimators give values close to the actual or true values. In addition, similar simulation experiments are also used to test the accuracy of a newly suggested procedure for estimating the standard errors of at‐site quantile estimators for the Hosking and Walls regional index flood method. The results of the simulations indicate that these estimated standard errors can in some cases give unreliable results. In general, this study shows that the PIF models are a useful addition to existing regional frequency analysis models. Their analytic structure, which is not present in other regional models, has important theoretical and practical implications.