Maximum likelihood estimators of population parameters from multiply censored samples

摘要

Left-censored data often arise in environmental contexts with one or more detection limits (DLs). Estimators of the parameters are derived for left-censored data having multiple detection limits: DL_1, DL_2,..., DL_k (k ≥3) assuming an underlying normal distribution. New method for calculating the maximum likelihood estimates (MLE) is given and examined for these cases. This method also applies to lognormally distributed environmental data with multiple distinct DLs. The performance of the new estimators is compared utilizing many simulated datasets. Examples are given illustrating the use of this method utilizing a computer program whose code is given in the Appendix section.