The generalized lambda distribution (gld) is a quantile defined distributional family that includes a very wide range of shapes within the one distributional form.

Recent work using L-Moments has provided insight into the shape properties of the distribution (Asquith, 2007, Karvanen,& Nuutinen, 2008). L-Moments are defined in terms of linear combinations of expectations of order statistics and exist whenever the first moment exists. Because the gld contains distributions with such heavy tails that the first moment does not exist, there is room in the field for a measure that exists even when the first moment does not. LQ-Moments (Mudholkar & Hutson, 1998) are analogous to L-Moments, but are based on quantile based location measures and exist for all distributions. This paper presents an LQ-Moment investigation into the shapes produced by the generalised lambda distribution. Results show that LQ Moments sensibly extend the L-Moment characterisation to the whole lambda3, lambda4 plane.

References:

Asquith, L-moments and TL-moments of the generalized lambda distribution, Computational Statistics & Data Analysis, 51(9), 2007, pp. 4484-4496

Karvanen,& Nuutinen, Characterizing the generalized lambda distribution by L-moments, Computational Statistics & Data Analysis, 52(4) 2008, pp 1971-1983

G. Mudholkar & Alan D. Hutson^, LQ-moments: Analogs of L-moments

Journal of Statistical Planning and Inference 71(1-2), 1998, pp 191-208.

Keywords: shape; generalized lamdba distribution; L Moments; Heavy tails

Biography: Dr King is a lecturer in statistics at the University of Newcastle, Australia.

His research interests include a range of quantile distributions, particularly in the areas of shape characterisation, estimation and modelling.