A Parameterization of the Generalized Lambda Distribution with Closed-Form Expressions for Method of L-Moment Estimation

• Activity Number: 457
• Type: Topic Contributed
• Date/Time: Wednesday, August 4, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Paul Jacobus van Staden*+
• Companies: University of Pretoria
• Keywords: Generalized lambda distribution ; Generalized Pareto distribution ; L-moment ratio diagram ; Quantile function

Abstract

In statistical modeling, two parameterizations of the generalized lambda distribution (GLD) have found favor among statisticians and practitioners, namely the Ramberg-Schmeiser (RS) and the Freimer-Mudholkar-Kollia-Lin (FMKL) parameterizations. Unfortunately, existing estimation methodologies for both these parameterizations are computationally difficult in that numerical optimization techniques are required. In this paper, using the generalized Pareto distribution as a building block, an alternative parameterization of the GLD is derived. Unlike the RS and FMKL parameterizations, this parameterization of the GLD has explicit formulae for the method of L-moment estimators. The properties of this parameterization are presented and its flexibility with respect to distributional shape is demonstrated through a number of illustrative examples.