Confidence Intervals based on Absolute Deviation for Population Mean of a Positively Skewed Distribution

Abstract

This paper proposes three alternative confidence intervals namely, AADM-t, MAAD-t and MADM-t, which are simple adjustments to the Student-t confidence interval for estimating the population mean of a positively skewed distribution. The proposed methods are very easy to calculate and are not overly computer-intensive. The performance of these confidence intervals was compared through a simulation study using the following criterion: (a) coverage probability (b) average width and (c) coefficient of variation of width. Simulation studies indicate that for small sample sizes and moderate/highly positively skewed distributions, the proposed AADM-t confidence interval performs the best and it is as good as the Student-t confidence interval. Some real-life data are analyzed which support the findings of this paper to some extent.