A Low-End Quantile Estimator from a Right-Skewed Distribution

• Activity Number: 83
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Paul Horn* and Hongjun Wang
• Companies: Cincinnati Children's Hospital Medical Center and University of Cincinnati
• Keywords: asymmetric distributions ; percentiles ; robust methods ; transformation ; order statistics ; nonpararmetrics

Abstract

In many statistical applications estimation of population quantiles is desired. In this study, a Log-Flip-Robust (LFR) approach is proposed to estimate, specifically, lower-end quantiles (those below the median) from a continuous, positive, right-skewed distribution. Characteristics of common right-skewed distributions suggest that a logarithm transformation (L) followed by flipping the lower half of the sample (F) allows for the estimation of the lower-end quantile using robust methods (R) based on symmetric populations. Simulations show that this approach is superior, in many cases, to the nonparametric approach based on the order statistics, while not suffering from the sample size restriction of the latter.