  The k-body Gaussian Embedded Ensemble of Random Matrices is considered for N
bosons distributed on two single-particle levels. When k = N, the ensemble is
equivalent to the Gaussian Orthogonal Ensemble (GOE), and when k = 2 it
corresponds to the Two-body Random Ensemble (TBRE) for bosons. It is shown that
the energy spectrum leads to a rank function which is of the form of a discrete
generalized beta distribution. The same distribution is obtained assuming N
non-interacting quasiparticles that obey the fractional exclusion statistics
introduced by Haldane two decades ago.
