Distribution of minimum distance among N random points in d dimensions
Mark S. Fischler · 2002
The Minimum Distance test in the DIEHARD suite for validating random number generators often indicates ''false positives,'' rejecting the quality of what is actually a good generator. A reason for this is presented. The test has enough sensitivity to detect the discrepancy between the approximate theoretical distribution of minimum distance used, and the actual distribution. We present next-order corrections to the theoretical expected distribution, for the 2-dimensional case used in DIEHARD and for higher dimensions. The corrected expectation will eliminate false positives arising from theoretical distribution discrepancies, at any practical test sensitivity level.