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.

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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

Tags

DTIC Thesaurus Topics

  • Air Force
  • Convolution
  • Discrete Distribution
  • Intervals
  • New York
  • Probability
  • Random Variables
  • Sequences
  • Standards
  • United States
  • United States Government
  • Universities

Fields of Study

  • Mathematics

Readers

  • Battery Technology and Engineering
  • Mathematical Modeling and Probability Theory.