Application of lossy compression methods involves the occurrence of distortions, so the problem of evaluating the level of these distortions is urgent. When using the DCT transformation, the main objective of quality assessment is selecting a statistical distribution model of the DCT coefficients of the image and the methods for estimating the parameters of the model.A universal method of estimating the level of distortions that arise due to JPEG compression of images of any structural content is developed in the paper. To determine the image quality, PSNR metric is used. A key feature of the proposed method lies in involving various statistical models for computing the quantization noise variance of the DCT coefficients. In particular, for models of the DCT coefficients in the form of the double gamma distribution and the generalized Cauchy distribution, calculation-handy expressions for the quantization noise variance of the DCT coefficients of JPEG images are obtained. Using the double gamma distribution to solve the above problem is first proposed.The well-known Laplacian model provides a relatively accurate estimation of PSNR only for those images that mostly consist of regions rich in small parts. While for the images, which contain significant regions of monotonicity, the model in the form of the double gamma distribution provides a much better result.The accuracy of the obtained theoretical expressions is confirmed by the results of experiments with grayscale JPEG images.