We have investigated the Bose-Einstein (BE) statistics behavior of the exciton-biexciton (EX-BEX) system during the photoluminescence decay processes at 5K in a (GaAs) 1 2 /(AlAs) 1 2 type-II superlattice. Owing to the long lifetime of the type-II exciton, which is of the order of microseconds due to the indirect transition nature, we have precisely evaluated the density relation between the EX and BEX from the line-shape analysis of time-resolved photoluminescence spectra. At an EX density around 1x10 1 0 /cm 2 , the BEX density suddenly increases with a threshold-like profile. This behavior is quantitatively explained by the framework of BE statistics of the EX-BEX system. It is demonstrated that the threshold-like increase of the BEX density is recurred by the incidence of a second-excitation pulse with a time delay, which leads to the dynamical control of the BE statistics behavior.