This work presents a study of the distribution of the grey matter (GM) and white matter (WM) in brain magnetic resonance imaging (MRI). The distribution of GM and WM is characterized using a mixture of α-stable distributions. A Bayesian α-stable mixture model for histogram data is presented and unknown parameters are sampled using the Metropolis-Hastings algorithm. The proposed methodology is tested in 18 real images from the MRI brain segmentation repository. The GM and WM distributions are accurately estimated. The α-stable distribution mixture model presented in this paper can be used as previous step in more complex MRI segmentation procedures using spatial information. Furthermore, due to the fact that the α-stable distribution is a generalization of the Gaussian distribution, the proposed methodology can be applied instead of the Gaussian mixture model, which is widely used in segmentation of brain MRI in the literature.