The mean and standard deviation of data, some of which are below the detection limit: an introduction to maximum likelihood estimation

In this article, the principle of maximum likelihood estimation (MLE) is in troduced. It is illustrated by an application of the maximum likelihood met hod for the estimation of the mean and standard deviation of a singly censo red data set. This is a data set for which some data are only known to be b elow a lower limit (left-censored) or above an upper limit (right-censored) . An example of the determination of an impurity in a raw material, where t he measurements are carried out around the detection limit and some of thes e fall below it, is given to illustrate the application of MLE to a singly censored data set. The maximum likelihood estimates of the mean and the sta ndard deviation of a censored data set are based on the mean and the varian ce of the numerically known data, the detection limit, the proportion of no n-numerical data and a constant lambda. (C) 2000 Elsevier Science B.V. All rights reserved.