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ABSTRACTMoment‐matching discrete distributions were developed by Miller and Rice (1983) as a method to translate continuous probability distributions into discrete distributions for use in decision and risk analysis. Using gaussian quadrature, they showed that an n‐point discrete distribution can be constructed that exactly matches the first 2n ‐ 1 moments of the underlying distribution. These moment‐matching discrete distributions offer several theoretical advantages over the typical discrete approximations as shown in Smith (1993), but they also pose practical problems. In particular, how does the analyst estimate the moments given only the subjective assessments of the continuous probability distribution? Smith suggests that the moments can be estimated by fitting a distribution to the assessments. This research note shows that the quality of the moment estimates cannot be judged solely by how close the fitted distribution is to the true distribution. Examples are used to show that the relative errors in higher order moment estimates can be greater than 100%, even though the cumulative distribution function is estimated within a Kolmogorov‐Smirnov distance less than 1%.

Decision analysts use sensitivity analysis to identify influential variables, to determine which input variables to model stochastically, and to characterize scenarios that could affect a change in the rank ordering of the alternatives. A frequently recommended sensitivity analysis technique is "one‐way" sensitivity analysis, which determines a variable's influence by the degree to which the objective function changes as that variable is varied while all other variables are held fixed. Disadvantages of one‐way analysis are that it measures the influence of only one variable at a time and it assumes independence among the input variables. Clearly, however, there are situations when dependencies exist among the input variables that could possibly affect the sensitivity analysis results. This research develops a strategy that incorporates dependence relations among the input variables into the sensitivity analysis using rank correlations. Only decision problems with a finite number of alternatives and continuous state variables are considered.