EX E(E(K] uy) ] u B(u,) (a + b)/2 Comparisons of the lognormal density function and the compound uniformlognormal density function are made in Fig. 2. Comparisons of the gamma density function and the compound uniform-gamma density function are made in Fig. 3. MONTE CARLO SIMULATIONS Random normal deviates were generated by the method suggested by Bell (1968) and then transformed to a lognormal deviate by x = exp (y). Random gamma deviates with nonintegral shape parameter were generated with the method presented by Fishman (1973). Briefly, the method involves summing k (= greatest integer of a) exponential variates, E(1), adding to this sum a product of a beta variate distributed as fe(a - k, 1 - a + k) and an exponential €(1), and multiplying the total by the parameter 8. Samples of size n = 5, 10, 20, 30, 50, and 100 were drawn from each of the lognormal and gamma distributions. All possible combinations of EX = 1, 5, 10, 50, and 100 and coefficient of variation of c = 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, and 2.0 were used for both distributions. These combinations give a total of 210 cases per distribution. Each case was replicated 1,000 times to estimate the bias and achieved coverage (proportion of replicates in which the constructed 95% confidence interval contained the true parameter value) for the two estimators discussed above. In addition, the average length of the confidence interval for E(x) was calculated for each estimator. Parameters were calculated from EX and c for the lognormal distribution i in (0741) u < Q as: 1/2 In [ (EX)*/ (e741) ] 615