Importance of Distributional Form in Characterizing Inputs to Monte Carlo Risk Assessments

The selection among distributional forms for inputs into uncertainty and variability (e.g., Monte Carlo) analyses is an important task. This paper considers the importance of distributional selection by examining the overall and tail behavior of the lognormal, Weibull, gamma, and inverse gaussian distributions. It is concluded that at low relative standard deviation (below 1), there is less of a difference between upper tail behavior among the distributions than at higher RSD values. Sample sizes in excess of 200 are required to reliably distinguish between distributional forms at the higher RSD values. The likelihood statistic appears to offer a reasonable approach to distributional discrimination, and it, or a similar approach, should be incorporated into distributional fitting procedures used in risk analysis.

[1]  Natalie W. Harrington,et al.  Recommended distributions for exposure factors frequently used in health risk assessment. , 1994, Risk analysis : an official publication of the Society for Risk Analysis.

[2]  D E Burmaster,et al.  Principles of good practice for the use of Monte Carlo techniques in human health and ecological risk assessments. , 1994, Risk analysis : an official publication of the Society for Risk Analysis.

[3]  D E Burmaster,et al.  Lognormal distributions for water intake by children and adults. , 1992, Risk analysis : an official publication of the Society for Risk Analysis.

[4]  W. R. Schucany,et al.  Generating Random Variates Using Transformations with Multiple Roots , 1976 .

[5]  R. F. Kappenman,et al.  On A method for selecting a distributional model , 1982 .

[6]  D. Burmaster,et al.  Estimated Distributions for Average Daily Consumption of Total and Self-Caught Fish for Adults in Michigan Angler Households , 1994 .

[7]  Michael A. Stephens,et al.  Goodness of fit for the extreme value distribution , 1977 .

[8]  Rick L. Edgeman.  Assessing the inverse Gaussian distribution assumption , 1990 .

[9]  Craig H. Benson,et al.  Probability Distributions for Hydraulic Conductivity of Compacted Soil Liners , 1993 .

[10]  Anthony J. Jakeman,et al.  Identification of a distributional model , 1985 .

[11]  R L Smith,et al.  Use of Monte Carlo simulation for human exposure assessment at a superfund site. , 1994, Risk analysis : an official publication of the Society for Risk Analysis.

[12]  C. Quesenberry,et al.  Selecting Among Probability Distributions Used in Reliability , 1982 .

[13]  David E. Burmaster,et al.  Lognormal Distributions for Fish Consumption by the General U.S. Population , 1994 .

[14]  Charles E. Antle,et al.  Discrimination Between the Log-Normal and the Weibull Distributions , 1973 .

[15]  Louis Anthony Cox,et al.  Dealing with Uncertainty: From Health‐Risk Assessment to Environmental Decision Making , 1992 .

[16]  H. K. Hsieh.  Estimating the critical time of the inverse Gaussian hazard rate , 1990 .

[17]  H. de Lasa,et al.  Gas holdups and bubble characteristics in a bubble column operated at high temperature , 1993 .