Mathematics and Statistics Vol. 8(6), pp. 711 - 720
DOI: 10.13189/ms.2020.080612
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Comparison of Parameter Estimators for Generalized Pareto Distribution under Peak over Threshold

Wilhemina Adoma Pels ^*, Atinuke Olusola Adebanji , Sampson Twumasi-Ankrah
Department of Statistics and Actuarial Science, Kwame Nkrumah University of Science and Technology, Kumasi, PMB, Ghana

ABSTRACT

The study focused on the Generalized Pareto Distribution (GPD) under the Peak Over Threshold approach (POT). Twenty-one estimation methods were considered for extreme value modeling and their performances were compared. Our goal is to identify the best method in various conditions by the use of a systematic simulation study. Some other estimators which were initially not created under the POT framework (NON-POT) were also compared concurrently with the ones under the POT framework. The simulation results under varying shape parameters showed the Zhang Estimator as "best" in performance for NON-POT in estimating both the shape and scale parameter for heavy-tailed cases. In the POT framework, the Zhang Estimator again performed "best" in estimating very heavy tails for the shape and very short tails for the scale regardless of the value of the scale parameter. When varying sample size, under the NON-POT framework, the Zhang estimator performed as "best" heavy-tailed whiles for the POT framework, the Pickands Estimator was "best" in performance at estimating the shape parameter for large sample sizes and the Zhang, small sample sizes.

KEYWORDS
Generalized Pareto Distribution, Peak over Threshold (POT), Shape Parameter, Scale Parameter

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Wilhemina Adoma Pels , Atinuke Olusola Adebanji , Sampson Twumasi-Ankrah , "Comparison of Parameter Estimators for Generalized Pareto Distribution under Peak over Threshold," Mathematics and Statistics, Vol. 8, No. 6, pp. 711 - 720, 2020. DOI: 10.13189/ms.2020.080612.

(b). APA Format:
Wilhemina Adoma Pels , Atinuke Olusola Adebanji , Sampson Twumasi-Ankrah (2020). Comparison of Parameter Estimators for Generalized Pareto Distribution under Peak over Threshold. Mathematics and Statistics, 8(6), 711 - 720. DOI: 10.13189/ms.2020.080612.