An Efficiency of Bootstrap Confidence Intervals for Coefficient of Quartile Variation

Abstract

The purpose of this research is to study the efficiency of bootstrap confidence intervals for coefficient of quartile variation in three methods, namely, Bonett Bootstrap (BB), Nonparametric Bootstrap (NB), and Parametric Bootstrap (PB) method when estimating the population of quartile from five quartile methods, i.e. Tukey, Moore and McCabe (M&M), Mendenhall and Sincich (M&S), Freund and Perles (F&P) and Minitab. The data cases are symmetrical (N(4, 1)), fairly symmetrical (LN(0, 0.25), G(9, 2)), moderately skewness (LN(0, 0.5), G(6, 1)), highly skewness (LN(0, 0.75), LN(0, 1), LN(0, 1.5), G(2, 0.5), G(0.5, 0.5)) with the various sizes of samples. The criteria of confidence interval are considered from coverage probability and the average width of confidence interval at confidence level of 0.95 by using Monte Carlo simulation. The result for confidence interval of BB method found that the population of quartile estimated by Minitab method performs better when distributions are N(4, 1) and LN(0, 0.25) at small level of sample and G(0.5, 0.5) in various sizes of samples. For confidence interval of NB method, quartile estimated by F&P method has an efficiency in several distributions, namely, N(4, 1), G(9, 2) and G(6, 1) at small levels of samples and LN(0, 0.75), LN(0, 1) and G(2, 0.5) in many levels of samples. For confidence interval of PB method performs better than quartile estimated by F&P method when distributions are N(4, 1), LN(0, 0.5), G(6, 1) and G(9, 2) at small levels of samples. It is also found that the PB confidence interval based on Minitab quartile method has an efficiency in various sizes of samples when distributions are LN(0, 1.5), LN(0, 1), LN(0, 0.75) and G(2, 0.5) distribution.