  We numerically study the level statistics of the Gaussian $\beta$ ensemble.
These statistics generalize Wigner-Dyson level statistics from the discrete set
of Dyson indices $\beta = 1,2,4$ to the continuous range $0 < \beta < \infty$.
The Gaussian $\beta$ ensemble covers Poissonian level statistics for $\beta \to
0$, and provides a smooth interpolation between Poissonian and Wigner-Dyson
level statistics. We establish the physical relevance of the level statistics
of the Gaussian $\beta$ ensemble by showing near-perfect agreement with the
level statistics of a paradigmatic model in studies on many-body localization
over the entire crossover range from the thermal to the many-body localized
phase. In addition, we show similar agreement for a related Hamiltonian with
broken time-reversal symmetry.
