Predicting a given pixel from surrounding neighbouring pixels is of great interest for several image processing tasks. Previous works focused on developing different Gaussian based models. Simultaneously, in real-world applications, the image texture and clutter are usually known to be non-Gaussian. In this paper, we develop a pixel prediction framework based on a finite generalized inverted Dirichlet (GID) mixture model that has proven its efficiency in several machine learning applications. We propose a GID optimal predictor, and we learn its parameters using a likelihood-based approach combined with the Newton-Raphson method. We demonstrate the efficiency of our proposed approach through a challenging application, namely image inpainting, and we compare the experimental results with related-work methods.