Confidence intervals for means of positively skewed distributions

The objective of this study is to compare interval estimation methods for population means of positively skewed distributions. The estimation methods are the interval estimation method with student-t statistics, the interval estimation method with Johnson’s statistics, the interval estimation method with Hall’s statistics and the interval estimation method with Chen’s statistics. Log-normal distribution and Weibull distribution are considered. The measures of skewness under the consideration are 1.0, 3.0, 5.0, respectively. The sample sizes are 10, 30, 50 and the confidence levels are 0.95. The consideration has two steps. First, the confidence level of interval estimation methods are not lower than the determined confidence level value. The second is the comparision of mean of lower confidence limit, mean of upper confidence limit and mean of confidence interval length. The experimental data are generated by the Monte Carlo Simulation technique. The confidence level of interval estimation method with Bootstrap is higher than the non-boot-strap. The interval estimation method with Johnson’s statistics is the optimum estimation method for the upper confidence interval and two-tailed confidence interval. The interval estimation method with Chen’s statistics is the optimum estimation method for the lower confidence interval. Commonly, the confidence level of interval estimation methods for upper confidence interval are varied by the measure of skewness butthe confidence level of interval estimation methods for lower confidence interval and two-tailed confidence interval are converted by the measure of skewness. The mean of lower confidence limit is varied by the sample size, on the other hand, the mean of upper confidence limit and mean of confidence interval length are converted by the sample size.