INFINITELY DIVISIBLE DISTRIBUTIONS, CONDITIONS FOR INDEPENDENCE, AND CENTRAL LIMIT THEOREMS,

Abstract

A discussion is given of some general results for a class of random vectors that often arise in the modeling of radar clutter interference. If a random variable is the sum of a large number of small, statistically independent components, it can under certain conditions be approximated by the normal distribution. When these conditions cannot be obtained, the random variable can be approximated by a member of a broader class of infinitely divisible (I.D.) random variables. Conditions for independence are developed and a new parameter defines dependence between non-normal components of two I.D. random variables. Central limit theorems for sequences of I.D. variables and sequences of sums of small independent random variables employ characterizations of normal and Poisson distributions. (Author)

Document Details

Document Type
Technical Report
Publication Date
May 01, 1969
Accession Number
AD0689158

Entities

People

  • Percy A. Pierre

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Clutter
  • Mathematics
  • Normal Distribution
  • Radar Clutter
  • Random Variables
  • Sequences

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Regression Analysis.
  • Sensor Fusion and Tracking Systems.