scholarly journals thresholdmodeling: A Python package for modeling excesses over a threshold using the Peak-Over-Threshold Method and the Generalized Pareto Distribution

2020 ◽  
Vol 5 (46) ◽  
pp. 2013
Author(s):  
Iago Lemos ◽  
Antônio Lima ◽  
Marcus Duarte
Keyword(s):  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Threshold Method ◽  
Generalized Pareto ◽  
Peak Over Threshold ◽  
Peak Over Threshold Method ◽  
Python Package

scholarly journals A multiple threshold method for fitting the generalized Pareto distribution and a simple representation of the rainfall process

2010 ◽  
Vol 7 (4) ◽  
pp. 4957-4994 ◽  
Author(s):  
R. Deidda
Keyword(s):  
Time Series ◽  
Distribution Function ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Daily Rainfall ◽  
Rainfall Time Series ◽  
Threshold Method ◽  
Generalized Pareto ◽  
Multiple Threshold ◽  
Optimum Threshold

Abstract. Previous studies indicate the generalized Pareto distribution (GPD) as a suitable distribution function to reliably describe the exceedances of daily rainfall records above a proper optimum threshold, which should be selected as small as possible to retain the largest sample while assuring an acceptable fitting. Such an optimum threshold may differ from site to site, affecting consequently not only the GPD scale parameter, but also the probability of threshold exceedance. Thus a first objective of this paper is to derive some expressions to parameterize a simple threshold-invariant three-parameter distribution function which is able to describe zero and non zero values of rainfall time series by assuring a perfect overlapping with the GPD fitted on the exceedances of any threshold larger than the optimum one. Since the proposed distribution does not depend on the local thresholds adopted for fitting the GPD, it will only reflect the on-site climatic signature and thus appears particularly suitable for hydrological applications and regional analyses. A second objective is to develop and test the Multiple Threshold Method (MTM) to infer the parameters of interest on the exceedances of a wide range of thresholds using again the concept of parameters threshold-invariance. We show the ability of the MTM in fitting historical daily rainfall time series recorded with different resolutions. Finally, we prove the supremacy of the MTM fit against the standard single threshold fit, often adopted for partial duration series, by evaluating and comparing the performances on Monte Carlo samples drawn by GPDs with different shape and scale parameters and different discretizations.

scholarly journals A multiple threshold method for fitting the generalized Pareto distribution to rainfall time series

2010 ◽  
Vol 14 (12) ◽  
pp. 2559-2575 ◽  
Author(s):  
R. Deidda
Keyword(s):  
Time Series ◽  
Distribution Function ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Daily Rainfall ◽  
Rainfall Time Series ◽  
Threshold Method ◽  
Generalized Pareto ◽  
Multiple Threshold ◽  
Optimum Threshold

Abstract. Previous studies indicate the generalized Pareto distribution (GPD) as a suitable distribution function to reliably describe the exceedances of daily rainfall records above a proper optimum threshold, which should be selected as small as possible to retain the largest sample while assuring an acceptable fitting. Such an optimum threshold may differ from site to site, affecting consequently not only the GPD scale parameter, but also the probability of threshold exceedance. Thus a first objective of this paper is to derive some expressions to parameterize a simple threshold-invariant three-parameter distribution function which assures a perfect overlapping with the GPD fitted on the exceedances over any threshold larger than the optimum one. Since the proposed distribution does not depend on the local thresholds adopted for fitting the GPD, it is expected to reflect the on-site climatic signature and thus appears particularly suitable for hydrological applications and regional analyses. A second objective is to develop and test the Multiple Threshold Method (MTM) to infer the parameters of interest by using exceedances over a wide range of thresholds applying again the concept of parameters threshold-invariance. We show the ability of the MTM in fitting historical daily rainfall time series recorded with different resolutions and with a significative percentage of heavily quantized data. Finally, we prove the supremacy of the MTM fit against the standard single threshold fit, often adopted for partial duration series, by evaluating and comparing the performances on Monte Carlo samples drawn by GPDs with different shape and scale parameters and different discretizations.

scholarly journals Comparison of Parameter Estimators for Generalized Pareto Distribution under Peak over Threshold

2020 ◽  
Vol 8 (6) ◽  
pp. 711-720
Author(s):  
Wilhemina Adoma Pels ◽  
Atinuke Olusola Adebanji ◽  
Sampson Twumasi-Ankrah
Keyword(s):  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Generalized Pareto ◽  
Peak Over Threshold ◽  
Parameter Estimators

Design Approach for CALM Buoy Moored Vessel in Squall Conditions

2016 ◽  
Author(s):  
Alison Brown ◽  
Ward Gorter ◽  
Mark Paalvast ◽  
Jelte Kymmell
Keyword(s):  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Mesoscale Convective Systems ◽  
Design Parameters ◽  
Convective Systems ◽  
Extreme Loads ◽  
Tropical Environments ◽  
Generalized Pareto ◽  
Peak Over Threshold ◽  
Mesoscale Convective

This paper focuses on examining the response of a vessel moored to a Catenary Anchor Leg Mooring (CALM) buoy in squall conditions. This type of mooring arrangement is typically a temporary mooring used for loading and offloading product or a temporary arrangement used during construction and typically selected for shallow water locations, often in tropical environments when conditions are otherwise relatively benign. Squalls are mesoscale convective systems that cause rapid increases in wind speed and are often associated with large changes in wind direction and also occur mostly in tropical environments. Hence for some locations squall events are the design drivers for this mooring arrangement and are particularly important due to the imperfect squall forecasts available to the industry. To understand the risks in a squall environment the vessel-CALM buoy system is modelled for a range of both squall conditions and associated environmental conditions, covering typical associated wave and current conditions by season and direction. A response-based approach is used to determine the design parameters for the extreme loads, extrapolated using a peak over threshold (POT) approach and using a Generalized Pareto Distribution (GPD), for the vessel-CALM buoy system. The method for this approach is described in detail and contrasted with previous industry approaches.

Uncertainties in extreme surge level estimates from observational records

2005 ◽  
Vol 363 (1831) ◽  
pp. 1377-1386 ◽  
Author(s):  
H.W van den Brink ◽  
G.P Können ◽  
J.D Opsteegh
Keyword(s):  
Wind Speed ◽  
Pareto Distribution ◽  
Climate Model ◽  
Generalized Pareto Distribution ◽  
Optimal Choice ◽  
Ensemble Simulations ◽  
The North ◽  
Generalized Pareto ◽  
Peak Over Threshold ◽  
The North Sea

Ensemble simulations with a total length of 7540 years are generated with a climate model, and coupled to a simple surge model to transform the wind field over the North Sea to the skew surge level at Delfzijl, The Netherlands. The 65 constructed surge records, each with a record length of 116 years, are analysed with the generalized extreme value (GEV) and the generalized Pareto distribution (GPD) to study both the model and sample uncertainty in surge level estimates with a return period of 10 4 years, as derived from 116-year records. The optimal choice of the threshold, needed for an unbiased GPD estimate from peak over threshold (POT) values, cannot be determined objectively from a 100-year dataset. This fact, in combination with the sensitivity of the GPD estimate to the threshold, and its tendency towards too low estimates, leaves the application of the GEV distribution to storm-season maxima as the best approach. If the GPD analysis is applied, then the exceedance rate, λ , chosen should not be larger than 4. The climate model hints at the existence of a second population of very intense storms. As the existence of such a second population can never be excluded from a 100-year record, the estimated 10 4 -year wind-speed from such records has always to be interpreted as a lower limit.

Inference on P(Y

2020 ◽  
Vol 72 (2) ◽  
pp. 89-110
Author(s):  
Manoj Chacko ◽  
Shiny Mathew
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Maximum Likelihood Estimators ◽  
Record Values ◽  
Asymptotic Distributions ◽  
Bayes Estimators ◽  
Generalized Pareto ◽  
Pareto Distributions ◽  
Generalized Pareto Distributions

In this article, the estimation of [Formula: see text] is considered when [Formula: see text] and [Formula: see text] are two independent generalized Pareto distributions. The maximum likelihood estimators and Bayes estimators of [Formula: see text] are obtained based on record values. The Asymptotic distributions are also obtained together with the corresponding confidence interval of [Formula: see text]. AMS 2000 subject classification: 90B25

scholarly journals The Gamma Generalized Pareto Distribution with Applications in Survival Analysis

2017 ◽  
Vol 6 (3) ◽  
pp. 141 ◽  
Author(s):  
Thiago A. N. De Andrade ◽  
Luz Milena Zea Fernandez ◽  
Frank Gomes-Silva ◽  
Gauss M. Cordeiro
Keyword(s):  
Monte Carlo Simulation ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Real Data ◽  
Model Parameters ◽  
Monte Carlo Simulation Study ◽  
Lorenz Curves ◽  
Generalized Pareto ◽  
Mathematical Properties ◽  
Pareto Model

We study a three-parameter model named the gamma generalized Pareto distribution. This distribution extends the generalized Pareto model, which has many applications in areas such as insurance, reliability, finance and many others. We derive some of its characterizations and mathematical properties including explicit expressions for the density and quantile functions, ordinary and incomplete moments, mean deviations, Bonferroni and Lorenz curves, generating function, R\'enyi entropy and order statistics. We discuss the estimation of the model parameters by maximum likelihood. A small Monte Carlo simulation study and two applications to real data are presented. We hope that this distribution may be useful for modeling survival and reliability data.

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