Estimation of return levels with the generalised F distribution

Abstract Estimation of return levels is crucial for risk assessment in the environmental sciences. Distributional assumptions influence tail behaviour and may affect both point estimates of return levels and their associated confidence intervals. In this paper, we investigate the flexible four-parameter Generalised F (GenF) distribution, which includes several conventional models as special cases. With emphasis on return levels, we compare GenF with the generalised extreme value (GEV) distribution through simulation studies and analyses of river discharge and significant wave height data. Upper-tail asymptotics of the GenF are examined in relation to GEV. Potential numerical challenges in fitting the GenF are discussed. Overall, both models yield similar return-level estimates up to 200 years, while differences mainly concern tail diagnostics and uncertainty quantification; GenF provides a flexible complement to the classical GEV framework.