Evaluation of contamination data with non-detects using censored distributions

When measuring concentration of chemical compounds, we often have to deal with a~situation when the resulting values are found below the limit of detection or limit of quantification of the determination method. In order to statistically evaluate such data, the method of maximum likelihood considering doubly left-censored samples is applied. As a model distribution of measured concentrations, Weibull distribution is considered. Moreover, considering the asymptotic properties of maximum likelihood estimates, concentrations of chemicals can be compared using Wald's test based on the expected Fisher information matrix. Here we show that the described statistical method allows for a better evaluation of the obtained experimental data than commonly used methods where all values below the detection limits are replaced by a~constant. These methods are used for an analysis of the worldwide commonly used synthetic musk compounds (nitro and polycyclic) which were extracted from the fish samples caught upstream (Group 1) and downstream (Group 2) from a high-capacity wastewater treatment plant.