Confidence intervals for quantiles using generalized lambda distributions

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. This technique can also be used to find confidence interval for the mode of a continuous data as well as comparing two data sets in terms of quantiles.