Effect of percent non-detects on estimation bias in censored distributions

Uniqueness of the problem surrounding non-detects has been a concern alike to researchers and statisticians dealing with summary statistics while analyzing censored data. To incorporate non-detects in the estimation process, a simple substitution by the MDL (method detection limit) and the maximum likelihood estimation method are routinely implemented as standard methods by US-EPA laboratories. In situations where numerical standards are set at or near the MDL by regulatory agencies, it is prudent and important to closely investigate both the variability in test measurements and the estimation bias, because an inference based on biased estimates could entail significant liabilities. Variability is understood to be not only inevitable but also an inherent and integral part of any chemical analysis or test. In situations where regulatory agencies fail to account for the inherently present variability of test measurements, there is a need for regulated facilities to seek remedial action merely as a consequence of inadequate statistical procedure. This paper utilizes a mathematical approach to derive the bias functions and resulting bias curves are developed to investigate the censored samples from a variety of probability distributions such as normal, log-normal, gamma, and Gumbel distributions. Finally, the bias functions and bias curves are also compared to the results obtained by using Monte Carlo simulations.