Characterizations of generalized hyperexponential distribution functions

1 January 1987

journal article
research article
Published by Taylor & Francis in Communications in Statistics. Stochastic Models

Vol. 3 (1) , 115-148
https://doi.org/10.1080/15326348708807049

Abstract

This paper examines in detail the class of generalized hyperexponential (GH) probability distribution functions. The family is compared to and contrasted with similar popular classes of distributions used in stochastic modeling. Each of these families arises from a desire to preserve the computationally attractive feature of “memorylessness” possessed by the exponential probability distribution while extending the representations to a broader class in order to approximate an arbitrary probability distribution function. Thus the simple structure and attractive properties of the GH probability distribution functions are presented with a view toward facilitating the mathematical operations which frequently occur in practice.

Keywords

This publication has 12 references indexed in Scilit:

Order Statistics
Wiley Series in Probability and Statistics, 2003
A geometric interpretation of the relations between the exponential and generalized Erlang distributions
Advances in Applied Probability, 1982
Closure of Phase Type Distributions Under Operations Arising in Reliability Theory
The Annals of Probability, 1982
Finite Mixture Distributions
Published by Springer Nature ,1981
Efficient algorithms to derive maximum-likelihood estimates for finite exponential and weibull mixtures
Computers & Operations Research, 1981
A Note on Sampling from Combinations of Distributions
IMA Journal of Applied Mathematics, 1971
On the Waiting Time in the Queuing System GI/G/1
The Annals of Mathematical Statistics, 1970
Sufficient Conditions for a Mixture of Exponentials to be a Probability Density Function
The Annals of Mathematical Statistics, 1969
A use of complex probabilities in the theory of stochastic processes
Mathematical Proceedings of the Cambridge Philosophical Society, 1955
Certain Fourier Transforms of Distributions
Canadian Journal of Mathematics, 1951