Affiliations: [a] Department of Statistics, Florida International University, Miami, FL 33199, USA. E-mail: [email protected] | [b] Department of Statistics, Florida International University, Miami, FL 33199, USA. E-mail: [email protected]
Abstract: This paper considers and compares Classical (Student-t, Johnson-t, Median-t, Mad-t), Bootstrap (Bootstrap-t, Bias-corrected Accelerated Bootstrap) and Transformations (T1, T3, Median T1 and Median T3) 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 T1, Median T1, T3 and Median T3 outperform other intervals in terms of coverage probability attaining the nominal. However, Mad-t, Mad T1, Mad T3, bootstrap-t and BCA performed better compared to others in the sense of shorter widths. It is also noted that the proposed Median T1, Median T3, Mad t, Mad T1 and Mad T3 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.
Keywords: Confidence intervals, Median t, Johnson t, simulation, skewness, width