Performance of Some Confidence Intervals for Estimating the Population Mean Under Contaminated Normal Distribution

This paper considers nine promising confidence interval estimators for estimating the population mean when the data are contaminated. A simulation study has been conducted to compare the performance of the interval estimators. The coverage probabilities and average widths of the interval estimators were considered as the performance criteria. The simulation results show that five out of nine interval estimators performed very well in terms of attaining high coverage probability and shorter average width. In addition, the DMSDDM-t confidence interval method tends to have a good performance for contaminated normal distributed data and a small sample size. For illustration purposes, three real-life data sets are analyzed which supported the findings obtained from the simulation study to some extent. The proposed confidence interval of the population mean can be easily calculated by using R program which is provided in the appendix.