  The generalised extreme value (GEV) distribution is a three parameter family
that describes the asymptotic behaviour of properly renormalised maxima of a
sequence of independent and identically distributed random variables. If the
shape parameter $\xi$ is zero, the GEV distribution has unbounded support,
whereas if $\xi$ is positive, the limiting distribution is heavy-tailed with
infinite upper endpoint but finite lower endpoint. In practical applications,
we assume that the GEV family is a reasonable approximation for the
distribution of maxima over blocks, and we fit it accordingly. This implies
that GEV properties, such as finite lower endpoint in the case $\xi>0$, are
inherited by the finite-sample maxima, which might not have bounded support.
This is particularly problematic when predicting extreme observations based on
multiple and interacting covariates. To tackle this usually overlooked issue,
we propose a blended GEV distribution, which smoothly combines the left tail of
a Gumbel distribution (GEV with $\xi=0$) with the right tail of a Fr\'echet
distribution (GEV with $\xi>0$) and, therefore, has unbounded support. Using a
Bayesian framework, we reparametrise the GEV distribution to offer a more
natural interpretation of the (possibly covariate-dependent) model parameters.
Independent priors over the new location and spread parameters induce a joint
prior distribution for the original location and scale parameters. We introduce
the concept of property-preserving penalised complexity (P$^3$C) priors and
apply it to the shape parameter to preserve first and second moments. We
illustrate our methods with an application to NO$_2$ pollution levels in
California, which reveals the robustness of the bGEV distribution, as well as
the suitability of the new parametrisation and the P$^3$C prior framework.
