Efficiency of composite sampling for estimating a lognormal distribution

In many environmental studies measuring the amount of a contaminant in a sampling unit is expensive. In such cases, composite sampling is often used to reduce data collection cost. However, composite sampling is known to be beneficial for estimating the mean of a population, but not necessarily for estimating the variance or other parameters. As some applications, for example, Monte Carlo risk assessment, require an estimate of the entire distribution, and as the lognormal model is commonly used in environmental risk assessment, in this paper we investigate efficiency of composite sampling for estimating a lognormal distribution. In particular, we examine the magnitude of savings in the number of measurements over simple random sampling, and the nature of its dependence on composite size and the parameters of the distribution utilizing simulation and asymptotic calculations.