Recently, image quality has been generally describedby a mean opinion score (MOS). However, we observe that thequality scores of an image given by a group of subjects are verysubjective and diverse. Thus it is not enough to use a MOS todescribe the image quality. In this paper, we propose to describeimage quality using a parameterized distribution rather thana MOS, and an objective method is also proposed to predictthe image quality score distribution (IQSD). At first, the LIVEdatabase is re-recorded. Specifically, we have invited a largegroup of subjects to evaluate the quality of all images in theLIVE database, and each image is evaluated by a large numberof subjects (187 valid subjects), whose scores can form a reliableIQSD. By analyzing the obtained subjective quality scores, wefind that the IQSD can be well modeled by an alpha stable model,and it can reflect much more information than a single MOS, suchas the skewness of opinion score, the subject diversity and themaximum probability score for an image. Therefore, we proposeto model the IQSD using the alpha stable model. Moreover, wepropose a framework and an algorithm to predict the alphastable model based IQSD, where quality features are extractedfrom each image based on structural information and statisticalinformation, and support vector regressors are trained to predictthe alpha stable model parameters. Experimental results verifythe feasibility of using alpha stable model to describe the IQSD,and prove the effectiveness of objective alpha stable model basedIQSD prediction method.