Mechanisms and techniques provide a system to evaluate operational integrity of a data processing system such as an area augmentation system by obtaining at least one set of distribution data related to information processed by the data processing system. The set(s) of distribution data can include corrections information and integrity bounds information related to the corrections information. The system applies a moment generating function to the set of distribution data to produce a moment bounded distribution data result and compares the moment bounded distribution data result to an integrity limit to determine if the data processing system operates within an acceptable integrity threshold. The system can be used in real-time or non-real time with sets of distribution data that are non-Gaussian, non-symmetric and/or non-unimodal.