Estimating the mean and variance of censored phosphorus concentrations in Florida rainfall

The total phosphorous (TP) concentrations in the South Florida rainfall have been recorded in weekly intervals with a detection limit (D-L) Of 3.5 mu g/L. As a large amount of the data is reported as below the D-L, appropriate statistical methods are needed for data analysis. Thus, an attempt was made to identify an appropriate method to estimate the mean and variance of the data. In particular a method to separate the statistics for the below D-L portion from the estimated population statistics is proposed. The estimated statistics of the censored data are compared with the statistics of the uncensored data available from the recent years' laboratory records. It was found that the one-step restricted maximum likelihood method is the most accurate for the wet TP data, and that the proposed method to combine the estimated statistics for TP < D-L portion and the sample statistics for TP > D-L portion improves estimates compared to the conventional maximum likelihood estimates.