Award Date

5-15-2026

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

First Committee Member

Hokwon Cho

Second Committee Member

Amei Amei

Third Committee Member

Zhijian Wu

Fourth Committee Member

Ian McDonough

Number of Pages

131

Abstract

A modified maximum likelihood estimation (MLE) algorithm is proposed for modeling threshold exceedances with the generalized Pareto distribution (GPD). The algorithm addresses multiple issues with an approach originally published in the Journal Computational Statistics and Data Analysis (Castillo and Serra, 2015). The modified algorithm is intended to be comparatively simple to understand and implement, accurate in the handling of boundary conditions, relatively fast and reliable for most data sets, and relatively easy to transfer between computer languages by leveraging existing optimization routines.

A reproducibility study of work in recent literature published in the journal Extremes (Belzile, et al., 2023) is conducted to evidence improved accuracy. Additionally, a subtle flaw in some existing software is revealed that was not previously discussed in the Belzile, et al. study. The modified algorithm is compared to existing methods (namely, the Grimshaw algorithm published in Technometrics, 1993), and potential advantages and disadvantages are discussed. Example programs are given in the R and Julia programming languages. The modified algorithm is used on an example dataset. The work also includes a modified implementation of the Grimshaw algorithm in the Julia programming language, and R code that returns the reproducibility study results.

Keywords

extreme value analysis; univariate peaks over threshold model

Disciplines

Physical Sciences and Mathematics | Probability | Statistics and Probability

File Format

PDF

File Size

1207 KB

Degree Grantor

University of Nevada, Las Vegas

Language

English

Rights

IN COPYRIGHT. For more information about this rights statement, please visit http://rightsstatements.org/vocab/InC/1.0/

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Probability Commons

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