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Based on the observation that a Cauchy density is more accurate in estimating the distribution of the ac coefficients than the traditional Laplacian density, rate and distortion models with improved accuracy are developed. The entropy and distortion models for quantized discrete cosine transform coefficients are justified in a frame bit-allocation application for H.264. Extensive analysis with carefully selected anchor video sequences demonstrates a 0.24-dB average peak signal-to-noise ratio (PSNR) improvement over the JM 8.4 rate control algorithm, and a 0.33-dB average PSNR improvement over the TM5-based bit-allocation algorithm that has recently been proposed for H.264 by Li et al. The analysis also demonstrates 20% and 60% reductions in PSNR variation among the encoded pictures when compared to the JM 8.4 rate control algorithm and the TM5-based bit-allocation algorithm, respectively.