Compound Random Variables

  • Authors:

  • Erol Peköz;Sheldon M. Ross

  • Affiliations:

  • School of Management, Boston University, Boston, MA 02215, pekoz@bu.edu;Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089, smross@usc.edu

  • Venue:
  • Probability in the Engineering and Informational Sciences
  • Year:
  • 2004

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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.