Probability Distributions of Minkowski Distances between Discrete Random Variables

Abstract

Minkowski distances are frequently used to indicate the similarity of two vectors in a n-dimensional space. This paper is about the probability distributions of Minkowski distances (e.g., City-block distances and Euclidean distances) between vectors in spaces spanned by n orthogonal, discrete valued axes. Formulas to compute the distributions of Minkowski distances are developed, critical values for tests of significance are tabled, and a normal approximation is examined. With the given information about the distributions of Minkowski distances a proper interpretation of empirical distance values should be facilitated.