Tail structure and extreme-value domain properties of the generalised F distribution

Estimation of return levels is central to risk assessment in the environmental sciences. Distributional assumptions determine tail behaviour and influence the magnitude of extreme quantiles. In this paper, we study the flexible four-parameter generalised F (GenF) distribution and derive first- and second-order asymptotic expansions for high return levels using its Beta representation. The expansions clarify the roles of the GenF shape parameters and the approach towards the asymptotic regime. Numerical illustrations show the relation between exact GenF quantiles and their asymptotic approximations, and demonstrate how finite-level accuracy depends on the parameter configuration.