Entropies of Partitions,

Abstract

Let (f sub i) be the frequency of occurrence of events in a universe with n distinguishable event categories, i=1,2,3,...,n, with Summation from 1 to n of (f sub i)=N. The entropy of this universe is then defined by H = minus summation from 1 to n of ((p sub i) log to the base 2 of (p sub i)) bits where the (p sub i)'s are the relative frequencies (P sub i) = (f sub i)/N. On the other hand, the collection of (f sub i)'s represents a particular partition of N into precisely n parts. Since in the majority of observations it is the (f sub i)'s that are directly measured, this Table gives the entropy for partitions (f sub i) for N up to 24 directly, supplies major help for calculating the entropy of partitions for N up to 48, and is useful for cases in which N is less or about 200. (Author)

Document Details

Document Type
Technical Report
Publication Date
Sep 30, 1970
Accession Number
AD0718148

Entities

People

  • H. Tuttle
  • K. Kokjer
  • W. R. Ashby

Organizations

  • University of Illinois Urbana–Champaign

Tags

DTIC Thesaurus Topics

  • Acquisition
  • Frequency
  • Observation

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Phased Array Antenna Design.