A New Modified Confidence Interval Estimator of Location Parameter for Skewed Distribution

A new modified confidence interval has been proposed which incorporates a new point estimator of the location parameter mean for skewed data distribution. Traditionally, the trimmed mean confidence interval estimator (Trm-ci) is a robust method for dealing with the skewness of the underlying data distribution. However, the Trm-ci method trims a certain fraction of endpoint observations to address skewness, which may result in a loss data information. The Students’t confidence interval (t-ci) estimator, while the most efficient estimator at normal models, becomes impractical in a situation where observed data is subject to non-normality due to robustness. In between the two, the median confidence interval estimator (Med-ci) is expected to retain the robustness of Trm-ci and the efficiency of t-ci. The idea behind the proposed new modified confidence interval estimator (Mod-ci) is to consider both the sample mean and sample median simultaneously, while also using end-point information without trimming any observations. As such, the proposed Mod-ci is expected to be as good as or better than other underlying methods regarding robustness and efficiency when dealing with skewed data distributions. In this study, we examine the performance of the new method compared to most commonly used methods through examples and simulating data from skewed distribution with varying degree of skewness. The results of examples and simulations suggest that the proposed method is as good as, or better than other estimators relevant to this study, as measured by estimated coverage probability and the width of associated confidence interval. Therefore, this method is recommended for practical application while dealing with real-life data exhibiting skewness.