Betting Against Stringency Mismatches in Standards and Limits: Monte Carlo Validation of Lognormally Based Quantile Conversions Between Sample Sizes

This paper proposes an updated procedure for estimating percentiles of arithmetic means of samples taken from lognormally distributed, autocorrelated populations. The updated procedure is intended for application in wastewater treatment plant discharge permitting and water quality standard rulemakings. Relative to the applicable guidance by the U.S. Environmental Protection Agency, the proposed updates allow the optional third (location) parameter of the lognormal distribution and accommodate samples of observations in non-consecutive time intervals for autocorrelated populations. The updated procedure was validated in simulations using synthetic autocorrelated lognormal data. The validation testing also showed that sample means from lognormal populations continue to be approximately lognormally distributed even for samples significantly larger than the sample size for which the normal distribution has previously been recommended. It is hoped that the updated procedure will be of practical use to the stakeholders in the increasing regulatory activity on nutrients in the U.S.