  Extreme-value distributions are studied in the context of a broad range of
problems, from the equilibrium properties of low-temperature disordered systems
to the occurrence of natural disasters. Our focus here is on the ground-state
energy distribution of disordered many-body quantum systems. We derive an
analytical expression that, upon tuning a parameter, reproduces with high
accuracy the ground-state energy distribution of the systems that we consider.
For some models, it agrees with the Tracy-Widom distribution obtained from
Gaussian random matrices. They include transverse Ising models, the Sachdev-Ye
model, and a randomized version of the PXP model. For other systems, such as
Bose-Hubbard models with random couplings and the disordered spin-1/2
Heisenberg chain used to investigate many-body localization, the shapes are at
odds with the Tracy-Widom distribution. Our analytical expression captures all
of these distributions, thus playing a role to the lowest energy level similar
to that played by the Brody distribution to the bulk of the spectrum.
