A low-end quantile estimator from a right-skewed distribution

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 current methods, while not suffering from the sample size restrictions of other approaches.

KEYWORDS:

• Asymmetric distributions
• Percentiles
• Robust methods
• Transformation

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G05, 62G30, 62G32, 62G35