On the Unimodality of High Convolutions.
Abstract
It has been conjectured, for any discrete density function on the integers, that there exists an n sub o such that the n-fold convolution is unimodal for all n > or = n sub o. A similar conjecture has been stated for continuous densities. We present several counterexamples to both of these conjectures. As a positive result, it is shown for a discrete density with a connected 3-point integer support that its n-fold convolution is fully unimodal for all sufficiently large n.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1980
- Accession Number
- ADA087079
Entities
People
- J. H. B. Kemperman
- Patrick L. Brockett
Organizations
- University of Texas at Austin