  In the beginning of the 1950's, Wigner introduced a fundamental deformation
from the canonical quantum mechanical harmonic oscillator, which is nowadays
sometimes called a Wigner quantum oscillator or a parabose oscillator. Also, in
quantum mechanics the so-called Wigner distribution is considered to be the
closest quantum analogue of the classical probability distribution over the
phase space. In this article, we consider which definition for such
distribution function could be used in the case of non-canonical quantum
mechanics. We then explicitly compute two different expressions for this
distribution function for the case of the parabose oscillator. Both expressions
turn out to be multiple sums involving (generalized) Laguerre polynomials.
Plots then show that the Wigner distribution function for the ground state of
the parabose oscillator is similar in behaviour to the Wigner distribution
function of the first excited state of the canonical quantum oscillator.
