On some classical,bootstrap and transformation confidence intervals for estimating the mean of an asymmetrical population

Abstract

This paper considers and compares Classical (Student-t, Johnson-t, Median-t, Mad-t), Bootstrap (Bootstrap-t, Bias-corrected Accelerated Bootstrap) and Transformations ( ${\mathit{T}}_1$ , ${\mathit{T}}_3$ , Median ${\mathit{T}}_1$ and Median ${\mathit{T}}_3$ ) approaches to find confidence intervals for estimating the mean of an asymmetrical distribution with unknown standard deviation. A simulation study has been made to compare the performance of the interval estimators by using average widths and coverage probabilities as performance estimators. For highly skewed distributions ${\mathit{T}}_1$ , Median ${\mathit{T}}_1$ , ${\mathit{T}}_3$ and Median ${\mathit{T}}_3$ outperform other intervals in terms of coverage probability attaining the nominal. However, Mad-t, Mad ${\mathit{T}}_1$ , Mad ${\mathit{T}}_3$ , bootstrap-t and BCA performed better compared to others in the sense of shorter widths. It is also noted that the proposed Median ${\mathit{T}}_1$ , Median ${\mathit{T}}_3$ , Mad t, Mad ${\mathit{T}}_1$ and Mad ${\mathit{T}}_3$ intervals are handy and easy to implement compared to others. Some health related data are considered to illustrate the findings of the paper. This paper gives more choices to use best possible interval estimators among many that have been used by several researchers.