  We present a formulation of the deformed oscillator algebra which leads to
intermediate statistics as a continuous interpolation between the Bose-Einstein
and Fermi-Dirac statistics. It is deduced that a generalized permutation or
exchange symmetry leads to the introduction of the basic number and it is then
established that this in turn leads to the deformed algebra of oscillators. We
obtain the mean occupation number describing the particles obeying intermediate
statistics which thus establishes the interpolating statistics and describe
boson like and fermion like particles obeying intermediate statistics. We also
obtain an expression for the mean occupation number in terms of an infinite
continued fraction, thus clarifying successive approximations.
