  A class of 2 X 2 random-matrix models is introduced for which the Brody
distribution is the exact eigenvalue spacing distribution. The matrix elements
consist of constrained sums of an exponential random variable raised to various
powers that depend on the Brody parameter. The random matrices introduced here
differ from those of the Gaussian Orthogonal Ensemble (GOE) in three important
ways: the matrix elements are not independent and identically distributed
(i.e., not IID) nor Gaussian-distributed, and the matrices are not necessarily
real and/or symmetric. The first two features arise from dropping the classical
independence assumption, and the third feature stems from dropping the
quantum-mechanical conditions that are imposed in the construction of the GOE.
In particular, the hermiticity condition, which in the present model, is a
sufficient but not necessary condition for the eigenvalues to be real, is not
imposed. Consequently, complex non-Hermitian 2 X 2 random matrices with real or
complex eigenvalues can also have spacing distributions that are intermediate
between those of the Poisson and Wigner classes. Numerical examples are
provided for different types of random matrices, including complex-symmetric
matrices with real or complex-conjugate eigenvalues.
