An Analysis of the Generalized Lambda Distribution
Abstract
The Generalized Lambda Distribution (GLD) is a four parameter function that is capable of mimicking the behavior of a wide range of probability density functions (pdfs). Unfortunately, the GLD presently cannot model every possible type of pdf. Since the reasons for this limitation are unknown, this thesis examines several potential problems in an attempt to expand the range of distributions the GLD can mimic. We first present a discussion of the behavior of the algorithm that is used to search for the appropriate GLD parameter values. In particular, we examine the effect of using an unconstrained search to find the parameters subject to a constraint that ensures that the resulting pdf is valid. We also develop a reparameterization of the GLD that creates an unconstrained search region. This does not expand the range of distributions the GLD can mimic. We then use an extensive numerical investigation to examine the set of distributions that can be obtained from combinations of the GLD parameters. This examination allows us to expand the range of pdfs that the GLD can model. We also inspect some pdfs that cannot be modeled using the GLD, as well as present an alternative to the method of moments for determining parameter values, using the concept of L-moments.... Generalized Lambda distribution (GLD), Powell's algorithm, Method of moments, L- moments.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1993
- Accession Number
- ADA262485
Entities
People
- Robert J. Bergevin
Organizations
- Air Force Institute of Technology