Confidence Intervals for Quantiles Using Generalized Lambda Distributions

• Activity Number: 383
• Type: Contributed
• Date/Time: Wednesday, August 1, 2007 : 8:30 AM to 10:20 AM
• Sponsor: Section on Risk Analysis
• Author(s): Steve Yu Shuo Su*+
• Companies: The George Institute for International Health
• Keywords: Generalised lambda distributions ; quantile confidence intervals ; density estimation ; risk analysis

Abstract

Generalized lambda distributions (GLD) can be used to fit a wide range of continuous data. As such, they can be very useful in estimating confidence intervals for quantiles of continuous data. This article proposes two simple methods (Normal-GLD approximation and the analytical-maximum likelihood GLD approach) to find confidence intervals for quantiles. These methods are used on a range of unimodal and bimodal data and on simulated data from ten well known statistical distributions (Normal, Student's T, Exponential, Gamma, Log Normal, Weibull, Uniform, Beta, F and Chi-square) with sample sizes n=10,25,50,100 for five different quantiles q=5%,25%,50%,75%,95%. In general, the analytical-maximum likelihood GLD approach works better with shorter confidence intervals and has closer coverage probability to the nominal level as long as the GLD models the data with sufficient accuracy.