scholarly journals Assessment of the Combined Effects of Threshold Selection and Parameter Estimation of Generalized Pareto Distribution with Applications to Flood Frequency Analysis

Water ◽  
2017 ◽  
Vol 9 (9) ◽  
pp. 692 ◽  
Author(s):  
Amr Gharib ◽  
Evan Davies ◽  
Greg Goss ◽  
Monireh Faramarzi
Keyword(s):  
Parameter Estimation ◽  
Frequency Analysis ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Combined Effects ◽  
Threshold Selection ◽  
Generalized Pareto

Comparison of Annual Maximum and Peaks Over Threshold Methods with Automated Threshold Selection in Flood Frequency Analysis: A Case Study for Australia

2021 ◽  
Author(s):  
Xiao Pan ◽  
Ataur Rahman
Keyword(s):  
Frequency Analysis ◽  
Flood Frequency ◽  
Distribution Functions ◽  
Flood Frequency Analysis ◽  
Annual Maximum ◽  
Threshold Selection ◽  
Peaks Over Threshold ◽  
Design Flood ◽  
Threshold Detection ◽  
Using Data

Abstract Flood frequency analysis (FFA) enables fitting of distribution functions to observed flow data for estimation of flood quantiles. Two main approaches, Annual Maximum (AM) and peaks-over-threshold (POT) are adopted for FFA. POT approach is under-employed due to its complexity and uncertainty associated with the threshold selection and independence criteria for selecting peak flows. This study evaluates the POT and AM approaches using data from 188 gauged stations in south-east Australia. POT approach adopted in this study applies a different average numbers of events per year fitted with Generalised Pareto (GP) distribution with an automated threshold detection method. The POT model extends its parametric approach to Maximum Likelihood Estimator (MLE) and Point Moment Weighted Unbiased (PMWU) method. Generalised Extreme Value (GEV) distribution using L-moment estimator is used for AM approach. It has been found that there is a large difference in design flood estimates between the AM and POT approaches for smaller average recurrence intervals (ARI), with a median difference of 25% for 1.01 year ARI and 5% for 50 and 100 years ARIs.

Penggunaan Taburan Pareto Umum dalam Menganalisis Nilai Ekstrim Banjir Menggunakan Siri Aliran Puncak Melebihi Paras

2012 ◽  
Author(s):  
Ani Shabri
Keyword(s):  
Poisson Process ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Annual Maximum ◽  
Peaks Over Threshold ◽  
Heavy Tailed Distributions ◽  
Probability Weighted Moment ◽  
Heavy Tailed

Siri banjir tahunan maksimum (Annual Maximum, AM) merupakan pendekatan yang begitu terkenal dalam analisis frekuensi banjir. Siri puncak melebihi paras (peaks over threshold, POT) telah digunakan sebagai alternatif kepada siri banjir tahunan maksimum. Masalah utama dalam pendekatan POT adalah berkaitan pemilihan paras yang sesuai. Dalam kajian ini, kesan perubahaan paras bagi siri POT ke atas nilai anggaran dikaji. Model POT dengan andaian bahawa bilangan puncak melebihi paras bertabur secara Poisson dan magnitud puncak melebihi paras tertabur secara Pareto Umum (General Pareto Distribution, GPD) dibincangkan. Parameter taburan GPD dianggar menggunakan kaedah kebarangkalian pemberat momen (Probability Weighted Moment, PWM) untuk paras yang diketahui. Perbandingan kesesuaian model POT dan model AM dalam menganggarkan nilai hujung atas taburan dibuat. Hasil kajian menunjukkan bahawa apabila paras siri POT boleh disuaikan oleh taburan Pareto dengan proses Poisson, model POT didapati dapat menghasilkan anggaran nilai hujung atas taburan lebih baik berbanding model aliran maksimum. Kata kunci: Siri puncak melebihi paras, proses poisson, taburan pareto umum, GEV, hujung atas taburan Annual maximum flood series remains the most popular approach to flood frequency analysis. Peaks over threshold series have been used as an alternative to annual maximum series. One specific difficulty of the POT approach is the selection of the threshold level. In this study the effect of raising the threshold of the POT series on heavy-tailed distributions estimation is investigated. The POT model described by the generalized Pareto distribution for peak magnitudes with the Poisson process for the occurrence of peaks is discussed. Estimation of the GPD parameters by the method of probability weighted moment (PWM) is formulated for known thresholds. A comparison of the efficiencies of the POT and AM models in heavy-tailed distributions is made. The result showed that when the threshold of POT series can be fitted by GPD with the Poisson process, the POT model is more efficient than the annual maximum (AM) model in estimating the highest extreme value. Key words: Peaks over threshold, poisson process, pareto distribution, GEV, heavy tailed distributions

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