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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
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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

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References

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