A methodology for incorporating risk and uncertainty considerations in the benefit-cost analysis of water resources projects is presented and illustrated with a case study. Estimates of benefits and costs are allowed to vary over ranges subjectively assessed, modeled as random variables with known probability density functions, and, finally aggregated analytically to yield a distribution of the B/C ratio. The advantages and limitations of this approach are discussed against a background of current guidelines by the U.S. Water Resources Council and existing U.S. Army Corps of Engineers procedures. Lemma 2. Let X•, X2, ß ß ß, Xn be statistically independent gamma random variables with parameters (ai, 13i) for i = 1, 2, ß ß ß , n. Then the new random variable Y = X• + X2 + ß ß ß + Xn has the moment generating function of form M(t) = [(1 -/3•t)"•(1 -•t) "2... (1 -lgnt)"n] -• (13) GOICOECHEA ET AL.' RISK/UNCERTAINTY IN BENEFIT-COST ANALYSIS 795 for all real t such that i3it < 1, where/3i = max {/3•, •, ß ß ß , The above results for lemmas 1 and 2 can be verified easily using the definition and unique properties of the moment generating function [Hogg and Craig, 1972]. Lemma 3. Let XB and Xc be two statistically independent normal random variables with parameters (/•i, ai 2) for i = B, C. Then, the new random variable Y = X•/Xc has the distribution g•) = y [4H: a•:ac:]ß ff• exp -• • + ac dz (14) for -• < Y < •. The proof is given in the appendix. Lemma 4. Let X• and Xc be two statistically independent gamma random variables with parameters (hi, •i) for i = B, C. Then the new random variable Y = X•c has the distribution
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