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Discrete Approximations of Probability Distributions


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  • Allen C. Miller, III

    (Practical Innovations, Inc., Sunnyvale, California)

  • Thomas R. Rice

    (ANR Technology Co., Detroit)

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    Practical limits on the size of most probabilistic models require that probability distributions be approximated by a few representative values and associated probabilities. This paper demonstrates that methods commonly used to determine discrete approximations of probability distributions systematically underestimate the moments of the original distribution. A new procedure based on gaussian quadrature is developed in this paper. It can be used to decrease the error in the approximation to any desired level.

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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 29 (1983)
    Issue (Month): 3 (March)
    Pages: 352-362

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    Handle: RePEc:inm:ormnsc:v:29:y:1983:i:3:p:352-362

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    Keywords: decision analysis; approximations; approximate probability distributions;


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    Cited by:
    1. Karl Mina & Gerald Cheang & Carl Chiarella, 2013. "Approximate Hedging of Options under Jump-Diffusion Processes," Research Paper Series 340, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Peck, Dannele E. & Adams, Richard M., 2010. "Farm-level impacts of prolonged drought: is a multiyear event more than the sum of its parts?," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 54(1), March.
    3. Peck, Dannele E. & Adams, Richard M., 2007. "The persistence of drought impacts across growing seasons: a dynamic stochastic analysis," 101st Seminar, July 5-6, 2007, Berlin Germany 9253, European Association of Agricultural Economists.
    4. Wall, A.D. & Worthington, D.J., 2007. "Time-dependent analysis of virtual waiting time behaviour in discrete time queues," European Journal of Operational Research, Elsevier, vol. 178(2), pages 482-499, April.
    5. Dasheng Ji & B. Brorsen, 2011. "A recombining lattice option pricing model that relaxes the assumption of lognormality," Review of Derivatives Research, Springer, vol. 14(3), pages 349-367, October.
    6. Tanaka, Ken’ichiro & Toda, Alexis Akira, 2013. "Discrete approximations of continuous distributions by maximum entropy," Economics Letters, Elsevier, vol. 118(3), pages 445-450.
    7. DeVuyst, Eric A. & Preckel, Paul V., 1997. "Sensitivity analysis revisited: A quadrature-based approach," Journal of Policy Modeling, Elsevier, vol. 19(2), pages 175-185, April.
    8. Liu, Songquan & Moskowitz, Herbert & Plante, Robert & Preckel, Paul V., 2002. "Product and process yield estimation with Gaussian quadrature (GQ) reduction: Improvements over the GQ full factorial approach," European Journal of Operational Research, Elsevier, vol. 140(3), pages 655-669, August.
    9. Horan, Richard D. & Claassen, Roger & Cooper, Joseph C., 2000. "Environmental Risk And Agri-Environmental Policy Design," 2000 Annual meeting, July 30-August 2, Tampa, FL 21827, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    10. David Abler & Adrián Rodríguez & James Shortle, 1999. "Parameter Uncertainty in CGE Modeling of the Environmental Impacts of Economic Policies," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 14(1), pages 75-94, July.
    11. Ji, Dasheng & Brorsen, B. Wade, 2000. "Increasing The Accuracy Of Option Pricing By Using Implied Parameters Related To Higher Moments," 2000 Conference, April 17-18 2000, Chicago, Illinois 18945, NCR-134 Conference on Applied Commodity Price Analysis, Forecasting, and Market Risk Management.
    12. Griffith, Marnie & Codner, Gary & Weinmann, Erwin & Schreider, Sergei, 2009. "Modelling hydroclimatic uncertainty and short-run irrigator decision making: the Goulburn system," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 53(4), December.
    13. Christopher Boyer & B. Brorsen & Tong Zhang, 2014. "Common-value auction versus posted-price selling: an agent-based model approach," Journal of Economic Interaction and Coordination, Springer, vol. 9(1), pages 129-149, April.


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