  The distributions of the spacing s between nearest-neighbor levels of
unfolded spectra of random matrices from the beta-Hermite ensemble (beta-HE) is
investigated by Monte Carlo simulations. The random matrices from the beta-HE
are real-symmetric and tridiagonal where beta, which can take any positive
value, is the reciprocal of the temperature in the classical electrostatic
interpretation of eigenvalues. Generalized gamma distributions are shown to be
excellent approximations of the nearest-neighbor spacing (NNS) distributions
for any beta while being still simple. They account both for the level
repulsion when s tends to zero and for the whole shape of the NNS distributions
in the range of s which is accessible to experiment or to most numerical
simulations. The exact NNS distribution of the GOE (beta=1) is in particular
significantly better described by a generalized gamma distribution than it is
by the Wigner surmise while the best generalized gamma approximation coincides
essentially with the Wigner surmise for beta larger than ~2. The distributions
of the minimum NN spacing between eigenvalues of matrices from the beta-HE,
obtained both from as-calculated eigenvalues and from unfolded eigenvalues are
Brody distributions.
