A Further Note on Generalized Hyperexponential Distributions
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 Erlang's early idea of modeling a duration or lifetime as a sum of independent and identical exponential stages. Much later, Jensen (1954) generalized Erlang's device to allow the stages to have non-identical CDFs, and indeed recognized the natural connection between Erlang's method of stages and absorption-time distributions of finite Markov chains. (KR)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 15, 1989
- Accession Number
- ADA214881
Entities
People
- Carl M. Harris
- Robert F. Botta
- William G. Marchal
Organizations
- George Mason University