Mean and Variance of Truncated Normal Distributions

Maximum likelihood estimators for the mean and variance of a truncated normal distribution, based on the entire sample from the original distribution, are developed. The estimators are compared with the sample mean and variance of the censored sample, considering only data remaining after truncation. The full- and censored-sample estimators are compared using simulation. It is seen that, surprisingly, the censored-sample estimators generally have smaller mean square error than have the full-sample estimators.