Statistical Inference for L-Moments of Specific, Common Distributions

• Activity Number: 87 - SPEED: Statistics in Sports; Physical Activity/Sleep Studies, and Nonparametrics Part 2
• Type: Contributed
• Date/Time: Sunday, July 28, 2019 : 4:00 PM to 4:45 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Timothy Shawn Anderson* and Christine Schubert Kabban and Fairul Mohd-Zaid
• Companies: Air Force Institute of Technology and Air Force Institute of Technology and Air Force Research Labs
• Keywords: Order Statistics; L-moments; Distributions; Confidence Intervals

Abstract

The use of L-moments in research is becoming more prevalent. Created about 28 years ago by J.R.M. Hosking, L-moments are linear combinations of order statistics, & as such, are less susceptible to outliers than traditional moments. Common applications of L-moments include regional frequency analysis, finance and network research. In 2004, formulas were derived for the exact variance of these non-traditional moments based upon specific distributions. In 2018, we derived sample size guidance and “quick” confidence interval estimates for L-moments and L-moments ratios, expanding the research from 2004 to additional distributions. These confidence intervals, based off a Wald interval, maintained alpha level coverage for the following distributions: normal, exponential, uniform, Pareto, & Gumbel. We expand on this work to examine joint confidence intervals for L-moments and L-moments ratios by means of a multivariate normal and non-parametric density estimation utilizing the known covariance, which was solved previously. This work will be compared to the current literature which reflects bootstrapped, and simultaneous Bonferroni intervals.