cancel
Showing results for 
Show  only  | Search instead for 
Did you mean: 
Choose Language Hide Translation Bar
An Empirical Semiparametric One-sided Confidence Bound for Lower Quantiles of Distributions with Positive Support

Authors

Caleb King (1), Peter Parker (2), Derek Young (3)

Affiliations

(1) JMP Statistical Discovery, (2) NASA, (3) University of Kentucky

Journal

Quality and Reliability Engineering International

Date Published

December 2023

Abstract

In many industries, the reliability of a product is often determined by a quantile of a distribution of a product's characteristics meeting a specified requirement. A typical approach to address this is to assume a parametric model and compute a one-sided confidence bound on the quantile. However, this can become difficult if the sample size is too small to reliably estimate such a parametric model. Linear interpolation between order statistics is a viable nonparametric alternative if the sample size is sufficiently large. In most cases, linear extrapolation from the extreme order statistics can be used, but can result in inconsistent coverage. In this work, we perform an empirical study to generate robust weights for linear extrapolation that greatly improves the accuracy of the coverage across a feasible range of distribution families with positive support. Our method is applied to two industrial datasets.

Citation

King CParker PYoung DSAn empirical semiparametric one-sided confidence bound for lower quantiles of distributions with positive supportQual Reliab Eng Int20231-18https://doi.org/10.1002/qre.3477