  The distribution of block maxima of sequences of independent and
identically-distributed random variables is used to model extreme values in
many disciplines. The traditional extreme value (EV) theory derives a
closed-form expression for the distribution of block maxima under asymptotic
assumptions, and is generally fitted using annual maxima or excesses over a
high threshold, thereby discarding a large fraction of the available
observations. The recently-introduced Metastatistical Extreme Value
Distribution (MEVD), a non-asymptotic formulation based on doubly stochastic
distributions, has been shown to offer several advantages compared to the
traditional EV theory. In particular, MEVD explicitly accounts for the
variability of the process generating the extreme values, and uses all the
available information to perform high-quantile inferences. Here we review the
derivation of the MEVD, analyzing its assumptions in detail, and show that its
general formulation includes other doubly stochastic approaches to extreme
value analysis that have been recently proposed.
