The modeling of wavelet subband histograms via the product Bernoulli distributions (PBD) has received a lot of interest and the PBD model has been applied successfully in texture image retrieval. In order to fully understand the usefulness and effectiveness of the PBD model and its associated signature, namely, the bit-plane probability (BP) signature on image processing applications, we discuss and investigate some of their statistical properties. These properties would help to clarify the sufficiency of the BP signature to characterize wavelet subbands, which, in turn, justifies its use in real time applications. We apply the BP signature on supervised texture classification problem and experimental results suggest that the weighted L1-norm (rather than the standard L1-norm) should be used for the BP signature. Comparative classification experiments show that our method outperforms the current state-of-the-art Generalized Gaussian Density approaches.