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Characterisation and Some Statistical Aspects of Univariate and Multivariate Generalise d Pareto Distributions

Tajvidi, Nader LU (1996)
Abstract
Extreme value theory is about the distributions of very large or

very small values in a time series or stochastic process. This has

numerous applications connected with environmental science, civil

engineering, materials science and insurance. A rather recent

approach for modelling extreme events is the so called peak over

threshold (POT) method. The generalised Pareto distribution (GPD) is

a two-parameter family of distributions which can be used to model

exceedances over a threshold.



This thesis consists of three papers. The main focus is on some

theoretical and applied statistical issues of univariate and

multivariate extreme... (More)
Extreme value theory is about the distributions of very large or

very small values in a time series or stochastic process. This has

numerous applications connected with environmental science, civil

engineering, materials science and insurance. A rather recent

approach for modelling extreme events is the so called peak over

threshold (POT) method. The generalised Pareto distribution (GPD) is

a two-parameter family of distributions which can be used to model

exceedances over a threshold.



This thesis consists of three papers. The main focus is on some

theoretical and applied statistical issues of univariate and

multivariate extreme value modelling. In the first paper we compare

the empirical coverage of standard bootstrap and likelihood-based

confidence intervals for the parameters and 90\%-quantile of the

GPD. By applying a general method of D.~N.~Lawley, small sample

correction factors for likelihood ratio statistics of the parameters

and quantiles of the GPD have been calculated. The article also

investigates the performance of some bootstrap methods for

estimation of accuracy measures of maximum likelihood estimators of

parameters and quantiles of the GPD.



In the second paper we give a multivariate analogue of

the GPD and consider estimation of parameters in some specific

bivariate generalised Pareto distributions (BGPD's). We generalise

two of existing bivariate extreme value distributions and study

maximum likelihood estimation of parameters in the corresponding

BGPD's. The procedure is illustrated with an application to a

bivariate series of wind data.



The main interest in the thesis has

been on practicality of the methods so when a new method has been

developed, it's performance has been studied with the help of both

real life data and simulations. In the third paper we use three

previous articles as examples to illustrate difficulties which might

arise in application of the theory and methods which may be used to

solve them. A common theme in these articles is univariate and

multivariate generalised Pareto distributions. However, the

discussed problems are of a rather general nature and demonstrate

some typical tasks in applied statistical research. We also discuss

a general approach to design and implementation of statistical

computations. (Less)
Please use this url to cite or link to this publication:
author
opponent
  • Davis, Richard, Department of Statistics Colorado State University
organization
publishing date
type
Thesis
publication status
published
subject
defense location
Chalmers, Bothenburg
defense date
1996-12-06 10:00
language
English
LU publication?
yes
id
629fb2ed-eaba-429c-8f26-587634607415 (old id 1701948)
date added to LUP
2010-11-02 10:23:26
date last changed
2016-09-19 08:45:15
@misc{629fb2ed-eaba-429c-8f26-587634607415,
  abstract     = {Extreme value theory is about the distributions of very large or<br/><br>
 very small values in a time series or stochastic process. This has<br/><br>
 numerous applications connected with environmental science, civil<br/><br>
 engineering, materials science and insurance. A rather recent<br/><br>
 approach for modelling extreme events is the so called peak over<br/><br>
 threshold (POT) method. The generalised Pareto distribution (GPD) is<br/><br>
 a two-parameter family of distributions which can be used to model<br/><br>
 exceedances over a threshold.<br/><br>
 <br/><br>
 This thesis consists of three papers. The main focus is on some<br/><br>
 theoretical and applied statistical issues of univariate and<br/><br>
 multivariate extreme value modelling. In the first paper we compare<br/><br>
 the empirical coverage of standard bootstrap and likelihood-based<br/><br>
 confidence intervals for the parameters and 90\%-quantile of the<br/><br>
 GPD. By applying a general method of D.~N.~Lawley, small sample<br/><br>
 correction factors for likelihood ratio statistics of the parameters<br/><br>
 and quantiles of the GPD have been calculated. The article also<br/><br>
 investigates the performance of some bootstrap methods for<br/><br>
 estimation of accuracy measures of maximum likelihood estimators of<br/><br>
 parameters and quantiles of the GPD.<br/><br>
<br/><br>
 In the second paper we give a multivariate analogue of<br/><br>
 the GPD and consider estimation of parameters in some specific<br/><br>
 bivariate generalised Pareto distributions (BGPD's). We generalise<br/><br>
 two of existing bivariate extreme value distributions and study<br/><br>
 maximum likelihood estimation of parameters in the corresponding<br/><br>
 BGPD's. The procedure is illustrated with an application to a<br/><br>
 bivariate series of wind data.<br/><br>
<br/><br>
 The main interest in the thesis has<br/><br>
 been on practicality of the methods so when a new method has been<br/><br>
 developed, it's performance has been studied with the help of both<br/><br>
 real life data and simulations. In the third paper we use three<br/><br>
 previous articles as examples to illustrate difficulties which might<br/><br>
 arise in application of the theory and methods which may be used to<br/><br>
 solve them. A common theme in these articles is univariate and<br/><br>
 multivariate generalised Pareto distributions. However, the<br/><br>
 discussed problems are of a rather general nature and demonstrate<br/><br>
 some typical tasks in applied statistical research. We also discuss<br/><br>
 a general approach to design and implementation of statistical<br/><br>
 computations.},
  author       = {Tajvidi, Nader},
  language     = {eng},
  title        = {Characterisation and Some Statistical Aspects of Univariate and Multivariate Generalise d Pareto Distributions},
  year         = {1996},
}