sample sizes (Fig. 5). 80% in all cases. Land (1972). The minimum achieved coverage is greater than These results are consistent with the findings of Lognormal Estimator for Gamma Distributed Data A major finding is that the bias of the lognormal estimator becomes large for gamma distributed data as a becomes small or c becomes large. In particular, a relative bias (100[Ave(E(x)) - EX]/EX) of about 25% is present for a = 1 (Fig. 6). The case a = 1 corresponds to the exponential distribution. The relative bias of the lognormal estimator becomes much worse for a < 1. This result would be expected because the shapes of the two distributions differ greatly for a < 1. However, even for c = 0.75 (o = 1.78), the relative bias of the lognormal estimator for gamma distributed data is about 6%. Also, the achieved coverage of the confidence interval begins to decrease for c = 1.0 and n = 100 (Fig. 6). Coverage becomes very poor for c > l. Gamma Estimator for Lognormally Distributed Data In contrast to the lognormal estimator for gamma distributed data, the gamma estimator for lognormal data does quite well. This estimator is unbiased, and so the simulations showed. Also, the achieved coverage of this estimator is good for small sample sizes (n = 5) (Fig. 7), whereas the coverage of the lognormal estimator is usually significantly less than the predicted 95% for n = 5. However, the average confidence interval width is usually greater for the arithmetic mean. The achieved coverage of the arithmetic mean drops as c increases, but never below 75%, even for n = 5 and c = 2. Also for c = 0.75, the average confidence interval length becomes about the same for the two estimators. Robustness The same general conclusions discussed in the preceding four sections also hold when the lognormal and gamma estimators are applied to a compound lognormal or gamma distribution with the expected value selected from a uniform distribution, The arithmetic mean still provides an unbiased estimate of EX in all cases, while the lognormal estimator provides an unbiased estimate when the variate is uniform-lognormal distributed, but not for the case when the variate is uniform-gamma distributed. Confidence interval coverage for both estimators is always greater than 70% when there is negligible bias. Generally, the arithmetic mean had better coverage for the smaller sample sizes, while the lognormal esti- mator had better coverage for n = 100. Also, the lognormal estimator tended to have better coverage when c > 1.0. Of course, the average confidence interval width was also greater for the lognormal estimator when the coverage was larger than the gamma estimator. For the case EX = 1.0 and uniform-lognormal data, Fig. 8 provides the reader with some feel for the relationship between sample size c and coverage for the two estimators considered. 620