Distribution of minimum distance among N random points in d dimensions

Fischler, Mark

Fermi National Accelerator Laboratory

关键词: Distribution;    Dimensions;    Sensitivity;    99 General And Miscellaneous//Mathematics, Computing, And Information Science;   

DOI  :  10.2172/794005
RP-ID  :  FERMILAB-TM-2170
RP-ID  :  AC02-76CH03000
RP-ID  :  794005

美国|英语

来源: UNT Digital Library

【 摘 要 】

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.