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On the Selection of Distributions for Stochastic Variables

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  • Fritz A. Seiler
  • Joseph L. Alvarez

Abstract

One of the main steps in an uncertainty analysis is the selection of appropriate probability distribution functions for all stochastic variables. In this paper, criteria for such selections are reviewed, the most important among them being any a priori knowledge about the nature of a stochastic variable, and the Central Limit Theorem of probability theory applied to sums and products of stochastic variables. In applications of these criteria, it is shown that many of the popular selections, such as the uniform distribution for a poorly known variable, require far more knowledge than is actually available. However, the knowledge available is usually sufficient to make use of other, more appropriate distributions. Next, functions of stochastic variables and the selection of probability distributions for their arguments as well as the use of different methods of error propagation through these functions are discussed. From these evaluations, priorities can be assigned to determine which of the stochastic variables in a function need the most care in selecting the type of distribution and its parameters. Finally, a method is proposed to assist in the assignment of an appropriate distribution which is commensurate with the total information on a particular stochastic variable, and is based on the scientific method. Two examples are given to elucidate the method for cases of little or almost no information.

Suggested Citation

  • Fritz A. Seiler & Joseph L. Alvarez, 1996. "On the Selection of Distributions for Stochastic Variables," Risk Analysis, John Wiley & Sons, vol. 16(1), pages 5-18, February.
    • Handle: RePEc:wly:riskan:v:16:y:1996:i:1:p:5-18
    DOI: 10.1111/j.1539-6924.1996.tb01432.x
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    References listed on IDEAS

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    1. Andrew E. Smith & P. Barry Ryan & John S. Evans, 1992. "The Effect of Neglecting Correlations When Propagating Uncertainty and Estimating the Population Distribution of Risk," Risk Analysis, John Wiley & Sons, vol. 12(4), pages 467-474, December.
    2. Ronald L. Iman & Jon C. Helton, 1988. "An Investigation of Uncertainty and Sensitivity Analysis Techniques for Computer Models," Risk Analysis, John Wiley & Sons, vol. 8(1), pages 71-90, March.
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    4. Peter K. LaGoy, 1989. "Significant Figures in Risk Assessment: More Caution Is Warranted," Risk Analysis, John Wiley & Sons, vol. 9(4), pages 431-432, December.
    5. Alexander I. Shlyakhter, 1994. "An Improved Framework for Uncertainty Analysis: Accounting for Unsuspected Errors," Risk Analysis, John Wiley & Sons, vol. 14(4), pages 441-447, August.
    6. Fritz A. Seiler, 1987. "Error Propagation for Large Errors," Risk Analysis, John Wiley & Sons, vol. 7(4), pages 509-518, December.
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    Cited by:

    1. Robert T. Bailey, 1997. "Estimation from Zero‐Failure Data," Risk Analysis, John Wiley & Sons, vol. 17(3), pages 375-380, June.
    2. Mark A. Burgman & David A. Keith & Terry V. Walshe, 1999. "Uncertainty in Comparative Risk Analysis for Threatened Australian Plant Species," Risk Analysis, John Wiley & Sons, vol. 19(4), pages 585-598, August.
    3. Powell, Mark R. & Wilson, James D., 1997. "Risk Assessment for National Natural Resource Conservation Programs," Discussion Papers 10859, Resources for the Future.
    4. Powell, Mark & Wilson, James, 1997. "Risk Assessment for National Natural Resource Conservation Programs," RFF Working Paper Series dp-97-49, Resources for the Future.

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