  The propagator and corresponding path integral for a system of identical
particles obeying parastatistics are derived. It is found that the statistical
weights of topological sectors of the path integral for parafermions and
parabosons are simply related through multiplication by the parity of the
permutation of the final positions of the particles. Appropriate
generalizations of statistics are proposed obeying unitarity and
factorizability (strong cluster decomposition). The realization of simple
maximal occupancy (Gentile) statistics is shown to require ghost states.
