Two parametric models for income and financial return distributions are presented.
There are the four-parameter normal Laplace (NL) and the five-parameter
generalized normal Laplace (GNL) distributions. Their properties are discussed;
furthermore, estimation of the parameters by the method of moments and maximum
likelihood is presented. The performances of fitting the two models to nine empirical
distributions of family income have been evaluated and compared against the four- and
five-parameter generalized beta2 (GB2) and generalized beta (GB) distributions
which had been previously claimed as best-fitting four- and five- parameter models
for income distribution. The results demonstrate that the NL distribution has better
performance than the GB and GB2 distributions with the GNL distribution providing
an even better fit. Limited application to data on financial log returns shows that the
fit of the GNL is comparable to the well-known generalized hyperbolic distribution.
However, the GNL suffers from a lack of closed-form expressions for its probability
density and cumulative distribution functions, and fitting the distribution numerically
is slow and not always reliable. The results of this thesis suggest a strong case
for considering the GNL family as parametric models for income data and possibly
for financial logarithmic returns.
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/1215 |
| Date | 01 October 2008 |
| Creators | Wu, Fan |
| Contributors | Reed, William J. |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | Available to the World Wide Web |
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