ESTIMATION OF EXPECTED VALUES OF ENVIRONMENTAL POLLUTANTS WITH LOGNORMAL AND GAMMA DISTRIBUTIONS G. C. White Los Alamos Scientific Laboratory Los Alamos, New Mexico ABSTRACT Concentrations of environmental pollutants tend to follow positively skewed frequency distributions. Two such density functions are the gamma and lognormal. Minimum-variance unbiased estimators of the expected value for both densities are available. The small-sample statistical properties of each of these estimators were compared for its own distribution, as well as the other distribution to check the robustness of the estimator. Results indicated that the arithmetic mean provides an unbiased estimator when the underlying density function of the sample is either lognormal or gamma, and that the achieved coverage of the confidence interval is greater than 75 percent for coefficients of variation less than two. Further, Monte Carlo simulations were conducted to study the robustness of the above estimators by simulating a lognormal or gamma distribution with the expected value of a particular observation selected from a uniform distribution before the lognormal or gamma observation is generated. Again, the arithmetic mean provides an unbiased estimate of expected value, and the achieved coverage of the confidence interval is greater than 75 percent for coefficients of variation less than two. INTRODUCTION The concentrations of environmental pollutants have been suggested to follow positively skewed frequency distributions by numerous researchers. In particular, Pinder and Smith (1975) investigated the goodness of fit of the lognormal, Weibull, exponential, and normal distributions to radiocesium concentrations in soil and biota. They found that the lognormal distribution fit the majority of the data sets. Giesy and Weiner (1977) found that the lognormal also tended to fit the concentrations of trace metals in fish better than the Weibull, exponential, or 609