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Probability Distributions of Minkowski Distances between Discrete Random Variables

Institute of Psychology University of Munich, Germany

Reinhold Rauh

Institute of Computer Science University of Freiburg, Germany

Werner Schubo

Institute of Psychology University of Munich, Germany

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.

Educational and Psychological Measurement, Vol. 53, No. 2, 379-398 (1993)
DOI: 10.1177/0013164493053002007


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