Multi-distribution regula-falsi profile likelihood method for nonstationary hydrological frequency analysis

The recently developed regula-falsi profile likelihood (RF-PL) method has potential for quantifying uncertainty in nonstationary hydrological frequency analysis. However, its applicability to diverse distributions is constrained and lacks comprehensive evaluation. This paper extends the RF-PL method to multiple distributions (Gumbel, Generalized Logistic (GLO), Generalized Normal (GNO), Log-Normal, Log-Pearson type III, and Pearson type III (PE3)) by introducing their reparametrized log-likelihood functions. The extended multi-distribution RF-PL (MD-RF-PL) method is systematically assessed in a simulation study and practical applications, covering diverse nonstationary scenarios, distributions, L-skewness (τ), and return periods, and compared with the bootstrap and/or the conventional PL as benchmarks. The findings indicate that the MD-RF-PL method is computationally comparable to the bootstrap method but overall superior in capturing the true quantiles with reasonably wide confidence intervals when τ = 0.1 (moderate tails) and 0.3 (heavy tails). However, when τ = 0.5 (very heavy tails), although the MD-RF-PL method is superior and roughly equivalent to the bootstrap method for GEV and GLO distributions, respectively, it is inferior for GNO and PE3 distributions, albeit avoiding the occasionally extremely wide confidence intervals of the bootstrap method. This low performance of the MD-RF-PL method is associated with numerical instability. Moreover, the MD-RF-PL method reduces the computational demand of the PL method by 94–99% without degrading its accuracy. Both the simulation study and the practical applications consistently support the preference of the MD-RF-PL method for distributions with moderate to heavy tails and highlight the need for improving its numerical stability for very heavy tails.