On the Representation of Probability Distributions as the Convolution of Symmetric and Completely Asymmetric Parts.

Abstract

Let F, G, and H be probability distributions on the line each having finite variance and suppose G is symmetric. F is completely asymmetric (c.as.) if the equation F = G*H implies G = delta sub 0, i.e. is degenerate. It's proven that F can always be written F = G*H where H is c.as., but this representation may not be unique. Examples of singular and absolutely continuous (with respect to Lebesgue measure) c.as. distributions are given. Some extensions of these ideas are mentioned. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1984
Accession Number
ADA140843

Entities

People

  • S. P. Ellis

Organizations

  • Massachusetts Institute of Technology

Tags

DTIC Thesaurus Topics

  • Convolution
  • Decomposition
  • Equations
  • Integrals
  • Massachusetts
  • Mathematics
  • Military Research
  • Monitoring
  • Probability
  • Probability Distributions
  • Sequences
  • Statistics
  • Word Processors

Fields of Study

  • Mathematics

Readers

  • Aerospace Propulsion Engineering.
  • Graph Algorithms and Convex Optimization.
  • Statistical inference.