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Risk analysis method by the extreme data of dependent exogenous variables

Tereshchenko Ihor, Tereshchenko Anton, Bilous Nataliya, Shtangey Svetlana, Warsza Zygmunt L.

Journal of Automation Mobile Robotics and Intelligent Systems

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2021

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Vol. 15, No. 3

44--53

EN

Many practical tasks of data multivariate statistical analysis from the standpoint of a risk-oriented process approach (in accordance with ISO 9001: 2015, 31000: 2018) requires the definition of the risk values for the dependent exogenous variables of some processes. This paper proposes the method, which consist of original stages sequence for calculating value-at-risk (VaR) or conditional-value-at-risk (CVaR) of dependent exogenous variables, presented of the extreme data frame of critical manufacture process parameters or other parameters, for example, extreme data of environmental monitoring and etc. Risk analysis method by the extreme data of dependent exogenous variables, presented of the data matrix, uses the result of solving the formalized problem of defines the tails parameters of the joint distributions of exogenous variables as components of a bivariate random variable. It can be argued that the tails parameters of the joint distributions of dependent exogenous variables make the validated corrections of the VaR and CVaR estimates for such variables. This method expands the practical application of extreme value theory for the value at risk analysis of any dependent variables as process parameters.

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Criteria for identifying maximum rainfall determined by the peaks-over-threshold (POT) method under the Polish Atlas of Rainfall Intensities (PANDa) project

Burszta-Adamiak Ewa, Licznar Paweł, Zaleski Janusz

Meteorology Hydrology and Water Management. Research and Operational Applications

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2019

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Vol. 7, Iss. 1

3--13

EN

Determination of rainfall maxima from long-term series is one of the more important tasks in urban hydrology. These maxima are useful both in designing land drainage systems and for flood protection in a catchment. The identification of rainfall maxima for the hierarchy of rainfall durations from 5 min to 4 320 min is a fundamental stage of the creation of the first version of the Polish Atlas of Rainfall Intensities (PANDa), which will ultimately be a source of updated and reliable information on design rainfall intensities for designing and modeling rainwater drainage and retention systems in Poland. One of the methods for identifying extreme rainfall events is to use criteria for selecting rainfall based on their depth for a given rainfall frequency and duration. Existing national experience in this respect is based on the results of analyses usually conducted with regard to records from single weather stations. This article presents the results of a study designed to verify the usefulness of the literature-based criteria for identifying rainfall maxima using the peaks-over-threshold (POT) method at a much broader nationwide scale. The study analyzed data from a previously created digital database of rainfall series, which includes 3 000 stationyears (consisting of a 30-year measurement series from 100 weather stations of the Institute of Meteorology and the Water Management - National Research Institute (IMGW-PIB). The study results show that as far as the investigated measurement series are concerned, the criteria based on the literature sources have limited application and can only be used for identifying the largest short-duration rainfall events. To determine rainfall maxima for all of the time intervals analyzed (from 5 minutes to 3 days), it was necessary to develop our own criteria that would allow the methodology for identifying extreme rainfall events to be standardized for all 100 stations.

3

Estimation of the distortion risk premium for heavy-tailed losses under serial dependence

Ouadjed H.

Opuscula Mathematica

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2018

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Vol. 38, no. 6

871--882

EN

In the actuarial literature, many authors have studied estimation of the reinsurance premium for heavy tailed i.i.d. sequences, especially for the Proportional Hazard (PH) due to Wang. The main aim of this paper is to extend this estimation for heavy tailed dependent sequences satisfying some mixing dependence structure. In this study we prove that the new estimator is asymptotically normal. The behavior of the estimator is examined using simulation for MA(1) process. Keywords: extreme value theory, mixing processes, tail index estimation.

4

The limiting behaviour of sums and maximums of iid random variables from the viewpoint of different observers

Krajka T. K., Rychlik Z.

Probability and Mathematical Statistics

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2014

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Vol. 34, Fasc. 2

237--252

EN

The limiting behaviour of observed and all random variables in the max limit schema was considered by Mladenović and Piterbarg (2006) and Krajka (2011). Here those results are generalised in two directions: we allow more than one observer and one superobserver; we consider the max limit schema as well as the sum limit schema.

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Extremes of moving averages and moving maxima on a regular lattice

Basrak B., Tafro A.

Probability and Mathematical Statistics

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2014

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Vol. 34, Fasc. 1

61--79

EN

We study the extremal behaviour of spatial moving averages and moving maxima on a regular discrete grid. Our main assumption is that these random fields are stationary and regularly varying with the tail index α > 0. Using the asymptotic theory for point processes we characterise the limiting behaviour of their extremes over an increasing grid. Our approach builds on the results of Davis and Resnick concerning linear processes. By analogy to the analysis of time series data, an appropriate Hill estimator of the tail index can be defined.We exhibit a sufficient condition for the consistency of this estimator in a certain class of spatial lattice models. Finally, we show that this condition holds for the models in our title.