On Performance of Confidence Interval Estimate of Mean for Skewed Populations: Evidence from Examples and Simulations

Abstract

The performances of confidence interval (CI) estimates of mean for skewed distributions are compared for three traditional methods and two newly proposed methods using coverage probability and confidence length for varying levels of skewness via simulations. Two real-life examples are incorporated to justify the applicability of the two newly proposed methods (trimmed t and modified trimmed t CIs), compared to the traditional methods (Student’s t mad t and median t CIs). From the results of examples and simulation study, it appears that with skewed distribution, the proposed trimmed t and modified trimmed t CIs are as good as mad t or median t CIs in coverage probability consideration. With lower % trimmed, trimmed and modified trimmed t CIs are identical or close to the Student’s t CI, and with increased % trimmed, they are identical or close to the median t CI.

Keywords: Student’s t, Mad t, Median t, Modified trimmed t, Coverage probability, Length of confidence interval.