Computational Problems Related to the Galton-Watson Process,

Abstract

An algorithm to compute the probability distributions of the successive generation sizes in a Galton-Watson process is presented. The distribution of the number of offspring of each individual is assumed to be of phase type. A probability distribution is of phase type if it can be identified as the distribution of the time till absorption in an absorbing finite Markov chain with appropriate initial conditions. A detailed analysis of the error due to truncation is given, as well as an application in a problem related to the M/G/1 queue. A second algorithm deals with the distribution of the maximum generation size before extinction. Several theorems on probability distributions of phase type are proved.

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1975
Accession Number
ADA008999

Entities

People

  • Marcel F. Neuts

Organizations

  • Purdue University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Absorption
  • Algorithms
  • Demographic Cohorts
  • Extinction
  • Markov Chains
  • Markov Processes
  • Mathematics
  • Probability
  • Probability Distributions
  • Random Variables
  • Truncation

Fields of Study

  • Mathematics

Readers

  • Materials Science and Engineering.
  • Mathematical Modeling and Probability Theory.