  In this paper, we first discuss the general properties of an
intermediate-statistics quantum bracket, $[ u,v]_{n}=uv-e^{i2\pi /(n+1)}vu$,
which corresponds to intermediate statistics in which the maximum occupation
number of one quantum state is an arbitrary integer, $n$. A further study of
the operator realization of intermediate statistics is given. We construct the
intermediate-statistics coherent state. An intermediate-statistics oscillator
is constructed, which returns to bosonic and fermionic oscillators respectively
when $n\to \infty $ and $n=1$. The energy spectrum of such an
intermediate-statistics oscillator is calculated. Finally, we discuss the
intermediate-statistics representation of angular momentum ($su(2)$) algebra.
Moreover, a further study of the operator realization of intermediate
statistics is given in the Appendix.
