Density Functions and Descriptive Statistics for Distance Measures in Cartesian Space

Abstract

This research provides density functions and descriptive statistics for the distance between points for basic shapes in Cartesian space. Both Euclidean and Rectilinear Distances are determined for these shapes. The shapes are in the unit line, the unit square, unit circle, unit sphere and unit triangle. In all instances, an exact, symbolic solution is sought, but there are four occasions where that is not possible—for these cases, a reasonable approximate solution is obtained. For each distance measure, mean, median and standard deviation measures are provided as well.