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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
Abstract #307479
Title: Statistical Inference for L-Moments of Specific, Common Distributions
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

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.

Authors who are presenting talks have a * after their name.

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