scholarly journals Uncertainties in return values from extreme value analysis of peaks over threshold using the generalised Pareto distribution

2021 ◽  
pp. 107725
Author(s):  
Philip Jonathan ◽  
David Randell ◽  
Jenny Wadsworth ◽  
Jonathan Tawn
Keyword(s):  
Pareto Distribution ◽  
Extreme Value ◽  
Extreme Value Analysis ◽  
Peaks Over Threshold ◽  
Value Analysis ◽  
Generalised Pareto Distribution

Modeling of Motor Vehicle Claims Using Extreme Value Methodology and Monte Carlo Stimulation: A Comparative Study

2008 ◽  
Vol 4 (4) ◽  
pp. 96-103
Author(s):  
S. Chandrasekhar
Keyword(s):  
Monte Carlo ◽  
Pareto Distribution ◽  
Motor Vehicle ◽  
Claim Data ◽  
Extreme Value ◽  
Extreme Value Analysis ◽  
Claim Amount ◽  
Insurance Claims ◽  
Value Analysis ◽  
Generalised Pareto Distribution

Motor Vehicle Insurance claims form a substantial component of Non life insurance claims and it is also growing with increasing number of vehicles on roads. It is also desirable to have an idea of what will be the likely claim amount for the coming future (Monthly, Quarterly, Yearly) based on past claim data. If one looks at the claim amount one can make out that there will be few large claims compared to large number of average and below average claims. Thus the distributions of claims do not follow a Symmetric pattern which makes it difficult using normal Statistical analysis. The methodology followed to analyze such data is known as Extreme value Analysis. Extreme value analysis is a general name which covers (i) Generalised Extreme Value (GEV) (ii) Generalised Pareto Distribution (GPD). Basically these techniques can deal with non symmetric shape of the distribution which is close to reality. Normally one fits a generalised Extreme Value distribution (GEV)/Generalised Pareto Distribution (GPD) and using parameters of fitted distribution future, forecast of likely losses can be predicted. Second method of analyzing such data is using methodology of simulation. Here we fit a Poisson distribution for arrival of claims and weibull/pareto/Lognormal for claim amount. Using Monte Carlo Simulation one combines both the distributions for future prediction of claim amount. This paper shows a comparison of the above techniques on motor vehicle claims data.

Robust extreme value analysis by semiparametric modelling of the entire distribution range

2021 ◽  
Author(s):  
Frank Kwasniok
Keyword(s):  
Exponential Family ◽  
Pareto Distribution ◽  
Transition Probability ◽  
Value Theory ◽  
Extreme Value ◽  
Distribution Range ◽  
Extreme Value Analysis ◽  
Value Analysis ◽  
Tail Inference ◽  
Generalised Pareto Distribution

<p>Traditional extreme value analysis based on the generalised extreme value (GEV) or the generalised Pareto distribution (GPD) suffers from two drawbacks: (i) Both methods are wasteful of data as only block maxima or exceedances over a high threshold are used and the bulk of the data is disregarded, resulting in a large uncertainty in the tail inference. (ii) In the peak-over-threshold approach the choice of the threshold is often difficult in practice as there are no really objective underlying criteria.<br>Here, two approaches based on maximum likelihood estimation are introduced which simultaneously model the whole distribution range and thus constrain the tail inference by information from the bulk data. Firstly, the bulk matching method models the bulk of the distribution with a flexible exponential family model and the tail with a GPD. The two distributions are linked together at the threshold with appropriate matching conditions. The threshold can be estimated in an outer loop also based on the likelihood function. Secondly, in the extended generalised Pareto distribution (EGPD) model for non-negative variables the whole distribution is modelled with a GPD overlaid with a transition probability density which is again represented by an exponential family. Appropriate conditions ensure that the model is in accordance with extreme value theory both for the lower and upper tail of the distribution. The methods are successfully exemplified on simulated data as well as wind speed and precipitation data.</p>

Frequentist and Bayesian extreme value analysis on the wildfire events in Greece

2020 ◽  
Author(s):  
Nikos Koutsias ◽  
Frank A. Coutelieris
Keyword(s):  
Extreme Value Theory ◽  
Extreme Values ◽  
Value Theory ◽  
Extreme Value ◽  
Extreme Value Analysis ◽  
Burned Area ◽  
Accurate Assessment ◽  
Peaks Over Threshold ◽  
Bayesian Approaches ◽  
Value Analysis

<p>A statistical analysis on the wildfire events, that have taken place in Greece during the period 1985-2007, for the assessment of the extremes has been performed. The total burned area of each fire was considered here as a key variable to express the significance of a given event. The data have been analyzed through the extreme value theory, which has been in general proved a powerful tool for the accurate assessment of the return period of extreme events. Both frequentist and Bayesian approaches have been used for comparison and evaluation purposes. Precisely, the Generalized Extreme Value (GEV) distribution along with Peaks over Threshold (POT) have been compared with the Bayesian Extreme Value modelling. Furthermore, the correlation of the burned area with the potential extreme values for other key parameters (e.g. wind, temperature, humidity, etc.) has been also investigated.</p>

Robust extreme value analysis: the bulk matching method

2020 ◽  
Author(s):  
Frank Kwasniok
Keyword(s):  
Exponential Family ◽  
Pareto Distribution ◽  
Likelihood Function ◽  
Atmospheric Model ◽  
Extreme Value ◽  
Extreme Value Analysis ◽  
High Threshold ◽  
Model Parameters ◽  
Value Analysis ◽  
Block Maxima

<p>Traditional extreme value analysis based on the generalised ex-<br>treme value (GEV) or generalised Pareto distribution (GPD) suffers<br>from two drawbacks: (i) Both methods are wasteful of data as only<br>block maxima or exceedances over a high threshold are taken into ac-<br>count and the bulk of the data is disregarded. (ii) Moreover, in the<br>GPD approach, there is no systematic way to determine the threshold<br>parameter. Here, all the data are fitted simultaneously using a gener-<br>alised exponential family model for the bulk and a GPD model for the<br>tail. At the threshold, the two distributions are linked together with<br>appropriate matching conditions. The model parameters are estimated<br>from the likelihood function of all the data. Also the threshold param-<br>eter can be determined via maximum likelihood in an outer loop. The<br>method is exemplified on wind speed data from an atmospheric model.</p>

scholarly journals Mapping the Hazard of Extreme Rainfall by Peaks over Threshold Extreme Value Analysis and Spatial Regression Techniques

2006 ◽  
Vol 45 (1) ◽  
pp. 108-124 ◽  
Author(s):  
Santiago Beguería ◽  
Sergio M. Vicente-Serrano
Keyword(s):  
Probability Model ◽  
Spatial Regression ◽  
Practical Interest ◽  
Extreme Rainfall ◽  
Threshold Value ◽  
Extreme Value ◽  
Extreme Value Analysis ◽  
Parameter Estimates ◽  
Peaks Over Threshold ◽  
Value Analysis

Abstract The occurrence of rainfalls of high magnitude constitutes a primary natural hazard in many parts of the world, and the elaboration of maps showing the hazard of extreme rainfalls has great theoretical and practical interest. In this work a procedure based on extreme value analysis and spatial interpolation techniques is described. The result is a probability model in which the distribution parameters vary smoothly in space. This methodology is applied to the middle Ebro Valley (Spain), a climatically complex area with great contrasts because of the relief and exposure to different air masses. The database consists of 43 daily precipitation series from 1950 to 2000. Because rainfall tends to occur highly clustered in time in the area, a declustering process was applied to the data, and the series of daily cluster maxima were used hereinafter. The mean excess plot and error minimizing were used to find an optimum threshold value to retain the highest records (peaks-over-threshold approach), and a Poisson–generalized Pareto model was fitted to the resulting series. The at-site parameter estimates (location, scale, and shape) were regressed upon a set of location and relief variables, enabling the construction of a spatially explicit probability model. The advantages of this method to obtain maps of extreme precipitation hazard are discussed in depth.

Modeling European hot spells using extreme value analysis

2014 ◽  
Vol 58 (3) ◽  
pp. 193-207 ◽  
Author(s):  
C Photiadou ◽  
MR Jones ◽  
D Keellings ◽  
CF Dewes
Keyword(s):  
Extreme Value ◽  
Extreme Value Analysis ◽  
Value Analysis ◽  
Hot Spells

scholarly journals Threshold selection in univariate extreme value analysis

Extremes ◽  
2021 ◽  
Author(s):  
Laura Fee Schneider ◽  
Andrea Krajina ◽  
Tatyana Krivobokova
Keyword(s):  
Mean Squared Error ◽  
Extreme Value ◽  
Hill Estimator ◽  
Small Samples ◽  
Extreme Value Analysis ◽  
Threshold Selection ◽  
Value Analysis ◽  
Wide Range ◽  
Asymptotic Mean Squared Error ◽  
The Hill

AbstractThreshold selection plays a key role in various aspects of statistical inference of rare events. In this work, two new threshold selection methods are introduced. The first approach measures the fit of the exponential approximation above a threshold and achieves good performance in small samples. The second method smoothly estimates the asymptotic mean squared error of the Hill estimator and performs consistently well over a wide range of processes. Both methods are analyzed theoretically, compared to existing procedures in an extensive simulation study and applied to a dataset of financial losses, where the underlying extreme value index is assumed to vary over time.

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