  The idea that a system obeying interpolating statistics can be described by a
deformed oscillator algebra has been an outstanding issue. This original
concept introduced long ago by Greenberg is the motivation for this
investigation. We establish that a q-deformed algebra can be used to describe
the statistics of particles (anyons) interpolating continuously between Bose
and Fermi statistics, i.e., fractional statistics. We show that the generalized
intermediate statistics splits into the Boson-like and Fermion-like regimes,
each described by a unique oscillator algebra. The B-anyon thermostatistics is
described by employing the q-calculus based on the Jackson derivative but the
F-anyons are described by ordinary derivatives of thermodynamics. Thermodynamic
functions of both B-anyons and F-anyons are determined and examined.
