Graduate Thesis Or Dissertation

 

Extreme value index estimation with applications to modeling extreme insurance losses and sea surface temperatures Public Deposited

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/1831cn812

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  • The extreme value index (EVI) links the generalized extreme value (GEV) distribution and the generalized Pareto (GP) distribution. These two distributions are fundamental in extreme value theory (EVT), with the GEV distribution being the only possible non-degenerate limiting distribution of properly normalized maxima of iid random variables, and the GP distribution appearing as the limit distribution of scaled excesses over high thresholds. The reciprocal of the EVI is know as the Pareto tail index (provided the EVI is positive). A new tail index estimator is proposed here that is obtained by matching general theoretical harmonic moments with corresponding empirical moments. Theoretical properties of the estimator are provided along with applications and a comparison to other tail index estimators. A tail index estimator suitable for partitioned data is also given. Having only partitioned data to work with is a circumstance sometimes faced by actuaries. Strengths and weaknesses of this estimator are explored through simulation. An application of the estimator to real world partitioned insurance data is given. The sign of the EVI is of interest when one is interested in testing whether or not a distribution has a bounded tail. In this work, the controversial thermostat hypothesis for sea surface temperature (SST) is investigated in this framework. A GP model using SST data from the western Pacific warm pool provides some evidence of a temperature upper bound between 31.2C and 32.0C. This estimate is compared those obtained elsewhere using the ocean heat budget and other physical models.
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