The robustness of confidence intervals for the mean of delta distribution

The delta distribution is a mixture of a lognormal distribution and a distribution degenerate at zero. Interval estimators of the mean of delta distribution were proposed and examined under full assumption of the model. In this dissertation, robustness of these estimators is studied by comparing coverage properties when the data are contaminated. Simulation models have been considered to accommodate two types of contaminants: (1) data from lognormal distribution with higher level of skewness and (2) data from similar skewed distribution such as gamma, Weibull or Birnbaum-Saunders distributions with the same mean and variance as the original lognormal distribution. In addition, two new methods are proposed. The first proposed method is driven by the notion of invariance property of robustness. That is, by providing robust point estimators, robust confidence interval is obtained. The second proposed method is a bootstrap procedure.