Application of a Weighted Sum of Order p to Distance Estimation

Distance functions are employed to estimate actual distances in a transportation network. The bp -norm, which is a weighted sum of order p, is a generalization of the weighted p -norm, a well-known distance-predicting function. We derive some mathematical properties of the new norm and of a goodness-of-fit criterion. These properties are used to develop computational procedures to determine the bestfitting parameter values of the bp -norm for a transportation network. We apply the new norm to 17 geographic regions and find significant improvements in the accuracy of distance estimations over the weighted p -norm.