A Method for Simulating Univariate and Multivariate Burr Type III and Type XII Distributions with Specified L-Moments and L-Correlations

• Activity Number: 78
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Mohan Dev Pant*+ and Todd Christopher Headrick
• Companies: Southern Illinois University at Carbondale and Southern Illinois University at Carbondale
• Keywords: Monte Carlo simulation ; L-moments ; L-correlation ; order statistics

Abstract

Burr Type III and Type XII distributions are mainly used in statistical modeling and for simulating non-normal distributions with conventional moments (e.g. Skew, Kurtosis). However, conventional moment-based estimators can (a) be substantially biased, (b) have high variance, or (c) be influenced by outliers. In this context, a characterization of Burr distributions through the method of L-moments is introduced. Specifically, equations are derived for determining the shape parameters associated with user specified L-moment ratios (e.g. L-Skew, L-Kurtosis). A procedure is developed for generating multivariate Burr distributions with arbitrary L-correlation matrices. Numerical examples are provided to show that L-moment based Burr distributions are superior to their conventional moment based analogs in the context of distribution fitting. Monte Carlo simulation results are provided to show