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COMPOUND RANDOM VARIABLES

Published online by Cambridge University Press:  01 October 2004

Erol Peköz  and
Sheldon M. Ross
Erol Peköz
Affiliation:
School of Management, Boston University, Boston, MA 02215, E-mail: [email protected]
Sheldon M. Ross
Affiliation:
Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089, E-mail: [email protected]
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Abstract

We give a probabilistic proof of an identity concerning the expectation of an arbitrary function of a compound random variable and then use this identity to obtain recursive formulas for the probability mass function of compound random variables when the compounding distribution is Poisson, binomial, negative binomial random, hypergeometric, logarithmic, or negative hypergeometric. We then show how to use simulation to efficiently estimate both the probability that a positive compound random variable is greater than a specified constant and the expected amount by which it exceeds that constant.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 18 , Issue 4 , October 2004 , pp. 473 - 484
Copyright
© 2004 Cambridge University Press

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References

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