Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-23T09:48:49.992Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Three-Moment Approximation of a General Distribution by a Coxian Distribution

Published online by Cambridge University Press:  27 July 2009

M. C. Van Der Heijden
M. C. Van Der Heijden
Affiliation:
Centre for Quantitative Methods Nederlandse Philips Bedrijven B. V. Eindhoven, The Netherlands
Get access Rights & Permissions [Opens in a new window]

Abstract

The Coxian-2 distribution is a very useful distribution for queuing and reliability analysis. It is important to know when a general probability distribution can be approximated by a Coxian-2 distribution by fitting the first three moments. For a positive random variable with a squared coefficient of variation larger than 1, a lower bound on its third moment is known for which a three-moment fit exists. To complete the figure, in this note lower and upper bounds on the third moment are derived when the squared coefficient of variation is between 0.5 and 1. Also, we characterize the C2-distributions that correspond to these bounds.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 2 , Issue 2 , April 1988 , pp. 257 - 261
Copyright
Copyright © Cambridge University Press 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Altiok, T. (1985). On the phase-type approximation of general distributions. IIE Transactions 17(2):110–116.CrossRefGoogle Scholar
Cox, D.R. (1955). A use of complex probabilities in the theory of stochastic processes. Proceedings of the Cambridge Philosophical Society 51:313–319.CrossRefGoogle Scholar
Tijms, H.C. (1986). Stochastic Modelling and Analysis: A Computational Approach. Chichester: Wiley.Google Scholar
Whitt, W. (1982). Approximating a point process by a renewal process I: two basic methods. Operations Research 30:125–147.CrossRefGoogle Scholar