The Analytic Hierarchy Process (AHP) is one of the most used multi-criteria techniques that can be used for decision-making problems; it depends on judgments of decision maker/expert about different alternatives using some criteria to make the best decision about these alternatives. However, the eigenvector method used for deriving the priorities in the AHP has been criticized due to its deterministic mechanism where the error in judgments is not taking into consideration. The main aims of this paper are first to discuss using of statistical method to obtain priority weights instead of the eigenvector method, and then apply this statistical method to define the priorities of regional allocation of public investment in Egypt. Seven criteria have been used in this study to judge seven alternatives (regions), where the local priority weights as well as their standard errors are calculated for the criteria and the alternatives with regard to the criteria, and then the final (global) priority weights are calculated for the alternatives. Final results of the application case revealed that regions of upper Egypt had the highest priority for investment allocation compared to the other regions.