Mean Width of a Regular Cross-Polytope
Metric Geometry
2016-03-15 v2 Probability
Abstract
The expected range of a sample of n+1 normally distributed variables is known to be related to the mean width of a regular n-simplex. We show that the expected maximum mu_n of a sample of n half-normally distributed variables is related to the mean width of a regular n-crosspolytope. Both of these relations have mean square counterparts. An expression for mu_5 is found and is believed to be new.
Cite
@article{arxiv.1112.0499,
title = {Mean Width of a Regular Cross-Polytope},
author = {Steven R. Finch},
journal= {arXiv preprint arXiv:1112.0499},
year = {2016}
}
Comments
11 pages