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Development of Bivariate Extreme Value Distributions for Applications in Marine Technology

Karpa, Oleh
Doctoral thesis
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http://hdl.handle.net/11250/302108
Utgivelsesdato
2015
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  • Institutt for marin teknikk [2352]
Sammendrag
The extreme value theory for applications in such a responsible branch of industry

as offshore and maritime engineering requires a robust, straightforward and reliable

method for estimating the statistics of extremes. A method must be able to

extract as much statistical information as possible from a recorded time series of

data. In addition, a method must be capable to utilize the information regarding

the temporal dependence structure of the process, as well as spatial dependence

characteristics of the given time series in the bivariate case.

In this thesis, a newly developed method for the purpose of predicting extremes

associated with the observed process is studied thoroughly and improved. The

method is referred to as the average conditional exceedance rate (ACER) method.

It avoids the problem of having to decluster the data to ensure independence,

which is a requisite component in the application of, for example, the standard

peaks-over-threshold (POT) method. Moreover, the ACER method is specifically

designed to account for statistical dependence between the sampled data points

in a precise manner. The proposed method also targets the use of sub-asymptotic

data to improve prediction accuracy. The research shows that the ACER method,

if properly implemented, is able to provide a statistical representation with error

bounds of the exact extreme value distribution given by the data. In the first

part of the thesis, the method is demonstrated in detail by application to both

synthetic and real environmental data. From a practical point of view, it appears to

perform better than the POT and block maxima methods, and, with an appropriate

modification, it is directly applicable to non-stationary time series.

In the second part of the thesis, the ACER method for estimation of extreme

value statistics is extended in a natural way to also cover the case of bivariate time

series. This is achieved by introducing a cascade of conditioning approximations

to the exact bivariate extreme value distribution. The results show that when the

cascade converges, an accurate empirical estimate of the extreme value distribution

can be obtained. It is also revealed that the possible functional representation of the

empirically estimated bivariate ACER surface can be derived from the properties

of the extreme-value copula.

In this thesis, application of the bivariate ACER method is substantially studied

for bivariate synthetic data. Finally, performance of the method is demonstrated

for measured coupled wind speed and wave height data as well as simultaneous

wind speed measurements from two separate locations.
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NTNU
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Doctoral thesis at NTNU;2015:169

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