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Three-Point Approximations for Continuous Random Variables

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  • Donald L. Keefer

    (Gulf Oil Corporation, Pittsburgh)

  • Samuel E. Bodily

    (University of Virginia, on leave at the University of Washington)

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    Abstract

    This paper compares a number of approximations used to estimate means and variances of continuous random variables and/or to serve as substitutes for the probability distributions of such variables, with particular emphasis on three-point approximations. Numerical results from estimating means and variances of a set of beta distributions indicate surprisingly large differences in accuracy among approximations in current use, with some of the most popular ones such as the PERT and triangular-density-function approximations faring poorly. A simple new three-point approximation, which is a straightforward extension of earlier work by Pearson and Tukey, outperforms the others significantly in these tests, and also performs well in related multivariate tests involving the Dirichlet family of distributions. It offers an attractive alternative to currently used approximations in a variety of applications.

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    File URL: http://dx.doi.org/10.1287/mnsc.29.5.595
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 29 (1983)
    Issue (Month): 5 (May)
    Pages: 595-609

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    Handle: RePEc:inm:ormnsc:v:29:y:1983:i:5:p:595-609

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    Related research

    Keywords: probability modeling; approximation; decision analysis;

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    Cited by:
    1. Graham, John R. & Harvey, Campbell R., 2005. "The long-run equity risk premium," Finance Research Letters, Elsevier, vol. 2(4), pages 185-194, December.
    2. Glaser, Markus & Weber, Martin, 2005. "Overconfidence and Trading Volume," SIFR Research Report Series 40, Institute for Financial Research.
    3. Moors, J.J.A. & Schuld, M.H. & Mathijssen, A.C.A., 1995. "A new method for assessing judgmental distributions," Research Memorandum 708, Tilburg University, Faculty of Economics and Business Administration.
    4. Kotz, Samuel & van Dorp, J. René, 2005. "A link between two-sided power and asymmetric Laplace distributions: with applications to mean and variance approximations," Statistics & Probability Letters, Elsevier, vol. 71(4), pages 383-394, March.
    5. Rosenbloom, E. S., 1997. "A probabilistic interpretation of the final rankings in AHP," European Journal of Operational Research, Elsevier, vol. 96(2), pages 371-378, January.
    6. Durbach, Ian N. & Stewart, Theodor J., 2012. "Modeling uncertainty in multi-criteria decision analysis," European Journal of Operational Research, Elsevier, vol. 223(1), pages 1-14.
    7. John R. Graham & Campbell R. Harvey, 2001. "Expectations of Equity Risk Premia, Volatility and Asymmetry from a Corporate Finance Perspective," NBER Working Papers 8678, National Bureau of Economic Research, Inc.
    8. Durbach, Ian N. & Stewart, Theodor J., 2009. "Using expected values to simplify decision making under uncertainty," Omega, Elsevier, vol. 37(2), pages 312-330, April.
    9. Mort Webster & Nidhi Santen & Panos Parpas, 2012. "An approximate dynamic programming framework for modeling global climate policy under decision-dependent uncertainty," Computational Management Science, Springer, vol. 9(3), pages 339-362, August.
    10. Durbach, Ian N. & Stewart, Theodor J., 2011. "An experimental study of the effect of uncertainty representation on decision making," European Journal of Operational Research, Elsevier, vol. 214(2), pages 380-392, October.
    11. Markus Glaser & Martin Weber, 2007. "Overconfidence and trading volume," The Geneva Papers on Risk and Insurance Theory, Springer, vol. 32(1), pages 1-36, June.
    12. Cho, Sungbin, 2009. "A linear Bayesian stochastic approximation to update project duration estimates," European Journal of Operational Research, Elsevier, vol. 196(2), pages 585-593, July.

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