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Simple Dependent Pairs of Exponential and Uniform Random Variables

Author

Listed:
  • A. J. Lawrance

    (University of Birmingham, Birmingham, United Kingdom)

  • P. A. W. Lewis

    (Naval Postgraduate School, Monterey, California)

Abstract

The accurate characterization of input processes for simulation models can require the representation of dependencies among input values. Results are presented on the generation of dependent exponential and uniform pairs of random variates. A random-coefficient linear function of two independent exponential variables yielding a third exponential variable is used in the construction of simple, dependent pairs of exponential variables. To model negative dependency, the constructions employ antithetic exponential variables. By employing negative exponentiation, the constructions yield simple multiplicative-based models for dependent uniform pairs. The ranges of dependency allowable in the models are assessed by correlation calculations, both of the product moment and Spearman types. Broad ranges within the theoretically allowable ranges are found. Because of their simplicity, all models are particularly suitable for simulation and are free of point and line concentrations of probabilities.

Suggested Citation

  • A. J. Lawrance & P. A. W. Lewis, 1983. "Simple Dependent Pairs of Exponential and Uniform Random Variables," Operations Research, INFORMS, vol. 31(6), pages 1179-1197, December.
    • Handle: RePEc:inm:oropre:v:31:y:1983:i:6:p:1179-1197
    DOI: 10.1287/opre.31.6.1179
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    Citations

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    Cited by:

    1. Zheng, Buhong & J. Cushing, Brian, 2001. "Statistical inference for testing inequality indices with dependent samples," Journal of Econometrics, Elsevier, vol. 101(2), pages 315-335, April.
    2. Kim, Bara & Kim, Jeongsim, 2011. "Representation of Downton’s bivariate exponential random vector and its applications," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1743-1750.
    3. Nadarajah, Saralees & Ali, M. Masoom, 2006. "The distribution of sums, products and ratios for Lawrance and Lewis's bivariate exponential random variables," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3449-3463, August.

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