The analysis of design wind speed estimates specified in the National Building Code of Canada

2007 ◽  
Vol 34 (4) ◽  
pp. 513-524 ◽  
Author(s):  
M D Pandey ◽  
Y An
Keyword(s):  
Wind Speed ◽  
Order Statistics ◽  
Extreme Value Theory ◽  
Gumbel Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Building Code ◽  
Peaks Over Threshold ◽  
Wind Speed Data ◽  
Design Wind Speed

The design wind pressures specified in the 2005 National Building Code of Canada (NBCC) have been derived from the Gumbel distribution fitted to annual maximum wind speed data collected up to early 1990s. The statistical estimates of the annual maxima method are affected by a relatively large sampling variability, since the method considers a fairly small subset of available wind speed records. Advanced statistical methods have emerged in recent years with the purpose of reducing both sampling and model uncertainties associated with extreme quantile estimates. The two most notable methods are the peaks-over-threshold (POT) and annually r largest order statistics (r-LOS), which extend the data set by including additional maxima observed in wind speed time series. The objective of the paper is to explore the use of advanced extreme value theory for updating the design wind speed estimates specified in the Canadian building design code. The paper re-examines the NBCC method for design wind speed estimation and presents the analysis of the latest Canadian wind speed data by POT, r-LOS, and annual maxima methods. The paper concludes that r-LOS method is an effective alternative for the estimation of extreme design wind speed.Key words: wind speed, extreme value theory, order statistics, return period, maximum likelihood method, peaks-over-threshold method, generalized extreme value distribution, Gumbel distribution, generalized Pareto distribution.

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.

scholarly journals Extreme Value Theory Applied to r Largest Order Statistics Under the Bayesian Approach

2019 ◽  
Vol 42 (2) ◽  
pp. 143-166 ◽  
Author(s):  
Renato Santos Silva ◽  
Fernando Ferraz Nascimento
Keyword(s):  
Monte Carlo ◽  
Order Statistics ◽  
Bayesian Approach ◽  
Extreme Value Theory ◽  
Likelihood Estimation ◽  
Value Theory ◽  
Extreme Value ◽  
Environmental Data ◽  
Heavy Tailed ◽  
The Bayesian Approach

Extreme Value Theory (EVT) is an important tool to predict efficient gains and losses. Its main areas of analyses are economic and environmental. Initially, for that form of event, it was developed the use of patterns of parametric distribution such as Normal and Gamma. However, economic and environmental data presents, in most cases, a heavy-tailed distribution, in contrast to those distributions. Thus, it was faced a great difficult to frame extreme events. Furthermore, it was almost impossible to use conventional models, making predictions about non-observed events, which exceed the maximum of observations. In some situations EVT is used to analyse only the maximum of some dataset, which provide few observations, and in those cases it is more effective to use the r largest-order statistics. This paper aims to propose Bayesian estimators' for parameters of the r largest-order statistics. During the research, it was used Monte Carlo simulation to analyze the data, and it was observed some properties of those estimators, such as mean, variance, bias and Root Mean Square Error (RMSE). The estimation of the parameters provided inference for its parameters and return levels. This paper also shows a procedure to the choice of the r-optimal to the r largest-order statistics, based on the Bayesian approach applying Markov chains Monte Carlo (MCMC). Simulation results reveal that the Bayesian approach has a similar performance to the Maximum Likelihood Estimation, and the applications were developed using the Bayesian approach and showed a gain in accurary compared with otherestimators.

scholarly journals Extreme value theory in emerging markets: Evidence from the Montenegrin stock exchange

2015 ◽  
Vol 60 (206) ◽  
pp. 87-116 ◽  
Author(s):  
Julija Cerovic ◽  
Vesna Karadzic
Keyword(s):  
At Risk ◽  
Stock Market ◽  
Extreme Value Theory ◽  
Value At Risk ◽  
Emerging Market ◽  
Value Theory ◽  
Extreme Value ◽  
Peaks Over Threshold ◽  
Threshold Method ◽  
Block Maxima

The concept of Value at Risk(VaR) estimates the maximum loss of a financial position at a given time for a given probability. This paper considers the adequacy of the methods that are the basis of extreme value theory in the Montenegrin emerging market before and during the global financial crisis. In particular, the purpose of the paper is to investigate whether the peaks-over-threshold method outperforms the block maxima method in evaluation of Value at Risk in emerging stock markets such as the Montenegrin market. The daily return of the Montenegrin stock market index MONEX20 is analyzed for the period January 2004 - February 2014. Results of the Kupiec test show that the peaks-over-threshold method is significantly better than the block maxima method, but both methods fail to pass the Christoffersen independence test and joint test due to the lack of accuracy in exception clustering when measuring Value at Risk. Although better, the peaks-over-threshold method still cannot be treated as an accurate VaR model for the Montenegrin frontier stock market.

A COMPARISON OF SOME UNIVARIATE MODELS FOR VALUE-AT-RISK AND EXPECTED SHORTFALL

2007 ◽  
Vol 10 (06) ◽  
pp. 1043-1075 ◽  
Author(s):  
CARLO MARINELLI ◽  
STEFANO D'ADDONA ◽  
SVETLOZAR T. RACHEV
Keyword(s):  
At Risk ◽  
Extreme Value Theory ◽  
Value At Risk ◽  
Value Theory ◽  
Extreme Value ◽  
Expected Shortfall ◽  
Stable Laws ◽  
Peaks Over Threshold ◽  
Threshold Method ◽  
Block Maxima

We compare in a backtesting study the performance of univariate models for Value-at-Risk (VaR) and expected shortfall based on stable laws and on extreme value theory (EVT). Analyzing these different approaches, we test whether the sum–stability assumption or the max–stability assumption, that respectively imply α–stable laws and Generalized Extreme Value (GEV) distributions, is more suitable for risk management based on VaR and expected shortfall. Our numerical results indicate that α–stable models tend to outperform pure EVT-based methods (especially those obtained by the so-called block maxima method) in the estimation of Value-at-Risk, while a peaks-over-threshold method turns out to be preferable for the estimation of expected shortfall. We also find empirical evidence that some simple semiparametric EVT-based methods perform well in the estimation of VaR.

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>

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.

Mode-decomposing Analysis of the Extreme Load in Hybrid Electric Vehicles Using Extreme Value Theory

2016 ◽  
Vol 10 (1) ◽  
pp. 136-147
Author(s):  
Jian Zhou ◽  
Jixin Wang ◽  
Hongbin Chen
Keyword(s):  
Extreme Value Theory ◽  
Hybrid Electric Vehicle ◽  
Hybrid Electric Vehicles ◽  
Gumbel Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
New Thought ◽  
Extreme Loads ◽  
Extreme Load ◽  
Hybrid Electric

In a hybrid electric vehicle (HEV), the hybrid system, which is equipped with an engine and a motor, is a key component. However, given the multimode characteristics of HEV, the original extreme load of the engine or motor is not independent and the random variables cannot be directly fitted by the extreme value theory (EVT). Thus, this paper proposes a mode-decomposing application method (MDAM) using EVT. Based on the method, three typical distributions, including the Fréchet distribution, the Gumbel distribution, and the Weibull distribution, were combined as a unified expression, and it was adopted to fit the extreme loads within different modes of HEV. By comparing the fitting results, especially the shapes of the curves, the distributions of the load under different modes vary from each other, so the feasibility and necessity of MDAM in HEV are proved, and a new thought for fitting the extreme load in HEV is provided, which will contribute to improve the fitting accuracy.

Sign in / Sign up

Export Citation Format

Share Document