As the dynamic range of displays keeps increasing, there is a need for reverse tone mapping methods, which aim at expanding the dynamic range of legacy low dynamic range images for viewing on higher dynamic range displays. While a number of strategies have been proposed, most of them are designed for well-exposed input images and are not optimal when dealing with ill-exposed (under- or over-exposed) content. Further, this type of content is more prone to artifacts which may arise when using local methods. In this work, we build on an existing, automatic, global reverse tone mapping operator based on a gamma expansion. We improve this method by providing a new way for automatic parameter calculation from the image statistics. We show that this method yields better results across the whole range of exposures.