The peak signal-to-noise ratio (PSNR) is one of the most popular video quality metrics. This ratio is computed using both original and processed images. We propose a new method to estimate the PSNR from an encoded bit stream without using original video sequences. In the proposed method, the transform coefficients of images or video frames are modeled by a generalized Gaussian distribution. By utilizing the model parameters of this distribution, the PSNR can be estimated. We also propose a fast method that can be used to estimate the model parameters of the original transform coefficient distribution using quantized transform coefficients as well as quantization information extracted from encoded bit streams. Experimental results with H.264 bit streams show that the proposed generalized Gaussian modeling method delivers better performance compared to the standard Laplacian modeling method when estimating the PSNR. The proposed method can be applied to image or video streams compressed with standard coding algorithms, such as MPEG-1, 2, 4, H.264, and JPEG. The proposed method can also be used for image or video quality monitoring systems on the receiver's side.