Comparison of the properties and the performance of the criteria used to evaluate the accuracy of distance predicting functions

Abstract

<p>Distance predicting functions may be used in a variety of applications for estimating travel distances between points. To evaluate the accuracy of distance predicting functions, goodness-of-fit criteria are employed. AD_f (Absolute Deviations), SD_f (Squared Deviations) and NAD_f (Normalized Absolute Deviations) are the three criteria that are mostly employed for modelling distances. In the literature some assumptions have been made about the properties of each criterion. In this paper we present statistical analyses performed to compare the three criteria from different perspectives. For this purpose the ℓ_k,p,θ norm was employed as the distance predicting function. First we analyse statistical properties of the prediction errors, and then we statistically compare the three criteria by using absolute normalized error distributions in seventeen geographical regions.</p>