A SIMPLE DERIVATION OF THE POSSION DISTRIBUTION

Abstract

One of the most important stochastic processes is the Poisson process, in which it is assumed that (a) the numbers of events occurring in nonoverlapping time intervals are independent; (b) the probability of one event's occurring during time dt is lambda dt + o(dt), where lambda is a constant, while the probability that two or more occur is o(dt). Using only the simplest kind of reasoning from probability theory, the Poisson distribution is deduced from the basic assumptions (a) and (b). Consequently, the need for viewing the Poisson distribution as a limiting case of some other distribution is obviated. In addition the technique used readily generalizes to the case in which lambda depends on t.

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Document Details

Document Type
Technical Report
Publication Date
Jun 11, 1953
Accession Number
AD0604222

Entities

People

  • Robert E. Kalaba

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Intervals
  • Mathematics
  • Probability
  • Random Variables
  • Reasoning
  • Stochastic Processes
  • Time Intervals

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Statistical inference.
  • Theoretical Analysis.