Sampling from a Triangular Population

The distributions of midrange, half-range, median and geometric mean of samples from a triangular population are derived. Mean, median, and midrange are compared as to their efficiency in estimating the single parameter of the population, which is the upper end of the range of the distribution. The best estimator of the parameter, however, is based on the maximum value in the sample, since it is derived from the likelihood function and is a sufficient statistic.