Title: Some more average distance results

Authors: Trevor S. Hale; Heather S. Lutz; Faizul Huq

Addresses: Department of Management, Marketing, and Business Administration, University of Houston-Downtown, Houston, Texas 77002, USA ' Supply Chain and Information Systems Department, The Pennsylvania State University, University Park, Pennsylvania 16802, USA ' Department of Management Systems, Ohio University, Athens, Ohio 45701, USA

Abstract: The purpose of this study is to present a taxonomy of expected distance functions (EDFs). An EDF is the expected (where expected is used in the strict probabilistic sense) distance formula for a given metric between two algebraically defined regions (e.g., the expected Euclidean distance between a semi-circle of radius r centred at (x₁, y₁) that has a known bivariate probability density function in r and θ and a line segment beginning at (x₂, y₂) and ending at (x₃, y₃) that has a known probability density function along its length). A modest library of EDFs for various metrics (rectilinear, Euclidean, Tchebychev, etc.) between pairs of common geometric shapes (e.g., lines, semi-circles, rectangles, etc.) is presented. The taxonomy of EDFs contained herein is by no means meant to be an exhaustive list. Indeed, it is limited in scope to those considered to be of practical importance to geographic information, transportation science, and mathematical modelling professionals.

Keywords: expected distance functions; EDFs; geographic distance estimation; spatial models; mathematical modelling; EDF taxonomy.

DOI: 10.1504/IJMOR.2017.083189

International Journal of Mathematics in Operational Research, 2017 Vol.10 No.3, pp.342 - 369

Received: 18 Apr 2015
Accepted: 05 Jun 2015
Published online: 22 Mar 2017 *

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