A Robust Nonparametric Yeo- Johnson- Transformation- Based Confidence Interval for Quantiles of Skewed Distributions

Document Type : Original Article

Authors

1 Assistant Professor at Department of Statistics Faculty of Business, Alexandria University

2 Lecturer at Department of Statistics Faculty of Business, Alexandria University

Abstract

The main goal of this paper is to introduce a new robust nonparametric confidence interval for population quantiles. To achieve this goal, a robustified version of an exact equal-tailed two-sided confidence interval for normal quantiles is first introduced. The proposed confidence interval uses the Yeo-Johnson family of power transformations to bring the data into approximate normality or at least symmetry. Calculating the robustified confidence interval using the transformed data then transforming back the lower and upper limits of the confidence interval, the new proposed robust nonparametric confidence interval for population quantile is obtained. Through a simulation study, the proposed confidence interval is evaluated and compared with some competitor existing confidence intervals. The criteria used to evaluate and compare the performance of confidence intervals are: the coverage probability (CP), the mean length of confidence intervals (ML), and the root mean squared deviations of confidence interval’s midpoints from the true population quantiles (RMSmdp) of the confidence intervals from the true population quantile. There are no sample size restrictions on the new proposed confidence interval. Simulation results show a significant outperformance of the proposed confidence interval compared to all other competitors under investigation.

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