Measurements consistency based Receiver Autonomous Integrity Monitoring (RAIM) is the main technique for monitoring the integrity of Global Satellite Navigation Systems (GNSS) at the user level. Existing RAIM algorithms utilize two tests, in the position domain, for RAIM availability and measurement domain, for failure detection. These tests involve the computation of three parameters: test statistic, decision threshold and protection level. The test statistic is based on the actual measurements in the form of the Sum of the Squared Errors (SSE). The decision threshold is chosen on the basis of the statistical characteristics of the SSE including the assumption that the errors are normally distributed. However, in practice residual error distributions exhibit heavier tails than predicted by the Gaussian model. Therefore, this paper challenges the normality assumption of the residual navigation errors in three ways. Firstly, it uses real data to assess its impact on the traditional RAIM algorithm. Secondly, it applies Extreme Value Theory (EVT) to the tails and derives the Generalised Extreme Value (GEV) distribution to capture residual navigation errors. Thirdly, it compares the performance of the traditional RAIM approach with that employing the GEV distribution. The results demonstrate that the GEV distribution has an important role to play in integrity monitoring and therefore, should be considered in the development of future integrity algorithms.