Accession Number:

ADA214881

Title:

A Further Note on Generalized Hyperexponential Distributions

Descriptive Note:

Technical rept.

Corporate Author:

GEORGE MASON UNIV FAIRFAX VA VOLGENAU SCHOOL OF INFORMATION TECHNOLOGY AND ENGINEERING

Report Date:

1989-11-15

Pagination or Media Count:

23.0

Abstract:

Many authors have used distribution functions related to the exponential staging formulation introduced by Erlang see Brockmeyer et al., 1948, with primary modifications over the years by Jensen 1954 and Cox 1955 . Much of the current popularity of such distributions is due to the work of Neuts and colleagues on the so-called phase-type family see, e.g., Neuts, 1975 a,b and 1981, exploiting relationships to the theory of Markov chains and putting the theory to effective computational use in a large variety of stochastic models. For purposes of clarity, we note the following relationships between these classes of cumulative distribution functions CDFs. Essentially, all of this stems from Erlangs early idea of modeling a duration or lifetime as a sum of independent and identical exponential stages. Much later, Jensen 1954 generalized Erlangs device to allow the stages to have non-identical CDFs, and indeed recognized the natural connection between Erlangs method of stages and absorption-time distributions of finite Markov chains. KR

Subject Categories:

  • Statistics and Probability
  • Operations Research

Distribution Statement:

APPROVED FOR PUBLIC RELEASE