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Bit-plane probability of data is a useful characteristic for many applications, such as entropy coding. Its value may vary according to the distribution of the data. In this paper, the bit-plane probability of data with generalized Gaussian distribution is analyzed. By studying the statistical characteristics of the sources and the bit-plane probability for Laplacian distribution, an approximated analytic description of bit-plane probability for generalized Gaussian distribution is presented. This approximation calculates the bit-plane probability with low computational cost. Simulation results show that, the proposed algorithm can well approximate the actual bit-plane probability. In addition, when the proposed algorithm is applied to audio bit-plane arithmetic coding, the coding efficiency is higher than that based on the Laplacian distribution assumption.