Parameter Estimations of the Generalized Extreme Value Distributions for Small Sample Size

Raziraaniza Roslan,Chin Su Na,Darmesah Gabda

doi:10.13189/ms.2020.081308

Raziraaniza Roslan, Chin Su Na + Show 1 more

Open Access

https://doi.org/10.13189/ms.2020.081308

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Journal: Mathematics and Statistics	Publication Date: Mar 1, 2020
Citations: 6	License type: cc-by

Affiliation: Universiti of Malaysia Sabah

Abstract

The standard method of the maximum likelihood has poor performance in GEV parameter estimates for small sample data. This study aims to explore the Generalized Extreme Value (GEV) parameter estimation using several methods focusing on small sample size of an extreme event. We conducted simulation study to illustrate the performance of different methods such as the Maximum Likelihood (MLE), probability weighted moment (PWM) and the penalized likelihood method (PMLE) in estimating the GEV parameters. Based on the simulation results, we then applied the superior method in modelling the annual maximum stream flow in Sabah. The result of the simulation study shows that the PMLE gives better estimate compared to MLE and PMW as it has small bias and root mean square errors, RMSE. For an application, we can then compute the estimate of return level of river flow in Sabah.

Highlights

Extreme Value Theory (EVT) is a statistics field that concentrates on any possible event that can be led to more extreme than it is normally happening
There are two approaches used when it comes to analyzing the extreme value, which is Block maxima (BM) and peak over the threshold (POT)
The aim of this study is to model the annual maximum stream flow using the Generalized Extreme Value (GEV) distribution focusing on small sample size data

Summary

Introduction

Extreme Value Theory (EVT) is a statistics field that concentrates on any possible event that can be led to more extreme than it is normally happening. We can use EVT in a specific location to estimate the frequency and cost of such events over a period of time. There are two approaches used when it comes to analyzing the extreme value, which is Block maxima (BM) and peak over the threshold (POT). In BM, the period will be divided into equal section and the maximum of each will be selected. The approach is usually going to pair with generalized extreme value (GEV). While POT will select every value that exceeds a certain threshold and this approach leads to generalized Pareto distribution (GPD) [1]

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