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