scholarly journals THE FULL TAILS GAMMA DISTRIBUTION APPLIED TO MODEL EXTREME VALUES

2017 ◽  
Vol 47 (3) ◽  
pp. 895-917 ◽  
Author(s):  
Joan del Castillo ◽  
Jalila Daoudi ◽  
Isabel Serra
Keyword(s):  
Extreme Value Theory ◽  
Pareto Distribution ◽  
Extreme Values ◽  
Dispersion Model ◽  
Value Theory ◽  
Quantitative Modelling ◽  
Exponential Distributions ◽  
Exponential Dispersion Model ◽  
Aggregate Loss ◽  
Very High

AbstractIn this paper, we introduce the simplest exponential dispersion model containing the Pareto and exponential distributions. In this way, we obtain distributions with support (0, ∞) that in a long interval are equivalent to the Pareto distribution; however, for very high values, decrease like the exponential. This model is useful for solving relevant problems that arise in the practical use of extreme value theory. The results are applied to two real examples, the first of these on the analysis of aggregate loss distributions associated to the quantitative modelling of operational risk. The second example shows that the new model improves adjustments to the destructive power of hurricanes, which are among the major causes of insurance losses worldwide.

Stochastic comparison of parallel systems with Pareto components

2021 ◽  
pp. 1-13
Author(s):  
Sameen Naqvi ◽  
Weiyong Ding ◽  
Peng Zhao
Keyword(s):  
Order Statistics ◽  
Extreme Value Theory ◽  
Pareto Distribution ◽  
Parallel Systems ◽  
Value Theory ◽  
Extreme Value ◽  
Stochastic Comparison ◽  
Shape Parameters ◽  
Scale Parameters ◽  
Dispersive Ordering

Abstract Pareto distribution is an important distribution in extreme value theory. In this paper, we consider parallel systems with Pareto components and study the effect of heterogeneity on skewness of such systems. It is shown that, when the lifetimes of components have different shape parameters, the parallel system with heterogeneous Pareto component lifetimes is more skewed than the system with independent and identically distributed Pareto components. However, for the case when the lifetimes of components have different scale parameters, the result gets reversed in the sense of star ordering. We also establish the relation between star ordering and dispersive ordering by extending the result of Deshpande and Kochar [(1983). Dispersive ordering is the same as tail ordering. Advances in Applied Probability 15(3): 686–687] from support $(0, \infty )$ to general supports $(a, \infty )$ , $a > 0$ . As a consequence, we obtain some new results on dispersion of order statistics from heterogeneous Pareto samples with respect to dispersive ordering.

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>

Extreme values of non-stationary random sequences

1986 ◽  
Vol 23 (04) ◽  
pp. 937-950 ◽  
Author(s):  
Jürg Hüsler
Keyword(s):  
Extreme Value Theory ◽  
Extreme Values ◽  
Value Theory ◽  
Extreme Value ◽  
Extremal Index ◽  
Stationary Case ◽  
Random Sequences ◽  
Similar Role ◽  
High Level

We extend some results of the extreme-value theory of stationary random sequences to non-stationary random sequences. The extremal index, defined in the stationary case, plays a similar role in the extended case. The details show that this index describes not only the behaviour of exceedances above a high level but also above a non-constant high boundary.

scholarly journals Extreme Value Theory and Large Fire Losses

1974 ◽  
Vol 7 (3) ◽  
pp. 293-310 ◽  
Author(s):  
G. Ramachandran
Keyword(s):  
Statistical Theory ◽  
Extreme Value Theory ◽  
Extreme Values ◽  
Value Theory ◽  
Extreme Value ◽  
Large Fire ◽  
Fire Insurance ◽  
Reinsurance Treaty

The statistical theory of extreme values well described by Gumbel [1] has been fruitfully applied in many fields, but only in recent times has it been suggested in connection with fire insurance problems. The idea originally stemmed from a consideration of the ECOMOR reinsurance treaty proposed by Thepaut [2]. Thereafter, a few papers appeared investigating the usefulness of the theory in the calculation of an excess of loss premium. Among these, Beard [3, 4], d'Hooge [5] and Jung [6] have made contributions which are worth studying. They have considered, however, only the largest claims during a succession of periods. In this paper, generalized techniques are presented which enable use to be made of all large losses that are available for analysis and not merely the largest. These methods would be particularly useful in situations where data are available only for large losses.

scholarly journals An Application of Extreme Value Theory to Learning Analytics: Predicting Collaboration Outcome from Eye-tracking Data

2017 ◽  
Vol 4 (3) ◽  
Author(s):  
Kshitij Sharma ◽  
Valérie Chavez-Demoulin ◽  
Pierre Dillenbourg
Keyword(s):  
Eye Tracking ◽  
Extreme Value Theory ◽  
Extreme Values ◽  
Value Theory ◽  
Extreme Value ◽  
Collaborative Problem Solving ◽  
Tracking Data ◽  
Previous Approach ◽  
The Mean

The statistics used in education research are based on central trends such as the mean or standard deviation, discarding outliers. This paper adopts another viewpoint that has emerged in Statistics, called the Extreme Value Theory (EVT). EVT claims that the bulk of the normal distribution is mostly comprised of uninteresting variations while the most extreme values convey more information. We applied EVT to eye-tracking data collected during online collaborative problem solving with the aim of predicting the quality of collaboration. We compare our previous approach, based on central trends, with an EVT approach focused on extreme episodes of collaboration. The latter occurred to provide a better prediction of the quality of collaboration.

scholarly journals ON THE TWO STEP THRESHOLD SELECTION FOR OVER-THRESHOLD MODELLING

2012 ◽  
Vol 1 (33) ◽  
pp. 42
Author(s):  
Pietro Bernardara ◽  
Franck Mazas ◽  
Jérôme Weiss ◽  
Marc Andreewsky ◽  
Xavier Kergadallan ◽  
...  
Keyword(s):  
Pareto Distribution ◽  
Extreme Values ◽  
Generalized Pareto Distribution ◽  
Value Theory ◽  
Water Levels ◽  
Distributed Data ◽  
Threshold Selection ◽  
The Past ◽  
Generalized Pareto ◽  
Selection For

In the general framework of over-threshold modelling (OTM) for estimating extreme values of met-ocean variables, such as waves, surges or water levels, the threshold selection logically requires two steps: the physical declustering of time series of the variable in order to obtain samples of independent and identically distributed data then the application of the extreme value theory, which predicts the convergence of the upper part of the sample toward the Generalized Pareto Distribution. These two steps were often merged and confused in the past. A clear framework for distinguishing them is presented here. A review of the methods available in literature to carry out these two steps is given here together with the illustration of two simple and practical examples.

scholarly journals Maximum Values of Frozen Soil’s Depth and Hoar Frost’s Thickness Estimated on the Basis of Extreme Values Theory

2018 ◽  
Vol 12 (2) ◽  
pp. 13-23
Author(s):  
Maria Nedealcov ◽  
Valentin Răileanu ◽  
Gheorghe Croitoru ◽  
Cojocari Rodica ◽  
Crivova Olga
Keyword(s):  
Risk Factors ◽  
Extreme Value Theory ◽  
Extreme Values ◽  
Gumbel Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Frozen Soil ◽  
Return Interval ◽  
The Mean ◽  
Extreme Values Theory

Abstract Extreme climatic phenomena present risk factors for agriculture, health, constructions, etc. and are studied profoundly these past years using extreme value theory. Several relation that describe positive extreme values’ probability Generalized Extreme Value and Gumbel distribution are presented in the article. As a example, we show the maps of characteristic and reference values of the maximum depth of the frozen soil and thickness of hoar-frost with a probability of exceeding per year equal to 0,02, which is equivalent to the mean return interval of 50 years. The obtained results could serve as a base for elaboration of national annexes in constructions.

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