Modeling of generalized families of probability distribution in the quantile statistical universe

Description

This thesis develops a methodology for the construction of generalized families of probability
distributions in the quantile statistical universe, that is, distributions specified in terms of their
quantile functions. The main benefit of the proposed methodology is that it generates
quantile-based distributions with skewness-invariant measures of kurtosis. The skewness and
kurtosis can therefore be identified and analyzed separately.
The key contribution of this thesis is the development of a new type of the generalized
lambda distribution (GLD), using the quantile function of the generalized Pareto distribution
as the basic building block (in the literature each different type of the GLD is incorrectly
referred to as a parameterization of the GLD – in this thesis the term type is used). The
parameters of this new type can, contrary to existing types, easily be estimated with method
of L-moments estimation, since closed-form expressions are available for the estimators as
well as for their asymptotic standard errors. The parameter space and the shape properties of
the new type are discussed in detail, including its characterization through L-moments. A
simple estimation algorithm is presented and utilization of the new type in terms of data
fitting and approximation of probability distributions is illustrated. / Thesis (PhD)--University of Pretoria, 2013. / gm2014 / Statistics / unrestricted

Links & Downloads

1. http://hdl.handle.net/2263/40265
2. Van Staden, PJ 2013, Modeling of generalized families of probability distribution in the quantile statistical universe, PhD thesis, University of Pretoria, Pretoria, viewed yymmdd <http://hdl.handle.net/2263/40265>
3. D14/4/87/gm

Tags

Generalized lambda distribution

L-moment

Quantile function

Skewness-invariant measure of kurtosis

UCTD

Additional Fields

Identifer	oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:up/oai:repository.up.ac.za:2263/40265
Date	January 2013
Creators	Van Staden, Paul Jacobus
Contributors	Boraine, H., [e-mail], King, Robert Arthur Ravencroft
Publisher	University of Pretoria
Source Sets	South African National ETD Portal
Language	English
Detected Language	English
Type	Thesis
Rights	© 2013 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.