Generalized linear image processing systems have been developed from physical image formation models, human visual perception models, and mathematical models. Although there have been many papers on the extension, parameterization, and symmetrization of some of these systems, what is lacking is a unified framework such that the development and study of such systems can be performed based on a common ground. In this paper, we propose a conceptual image sensor which models how the light energy is converted into the sensor data. In the proposed sensor model, the input energy is regarded as a random variable and the conversion is through the cumulative distribution function. Based on the sensor model, we suggest a statistical framework by which new systems can be derived, and existing and seemingly unrelated systems can be studied from a unified perspective. The proposed statistical framework not only provides a principled way to symmetrizing systems through the even extension of the probability distribution function (PDF) and a natural way for the parameterization of systems through parameters of PDF. In this paper, we demonstrate new applications of the statistical framework through a numerical approximation of the lower incomplete gamma function, through the enhancement of the dynamic range and manipulation of the sharpness of images by using the scalar multiplication operation of the parametric system, through an application of a new system in fusion of multi-exposure images, and through an application of the three new systems for the correction of incorrect exposure.