Bivariate Extreme Research Articles

Loss Minimization Control Based on Bivariate Extreme Value Theory for PMSMs

Loss Minimization Control Based on Bivariate Extreme Value Theory for PMSMs

Effect of vehicle size on crash risk in a heterogeneous traffic scenario: a bivariate extreme value approach

ABSTRACT Most traffic conflict indicators are defined for car-following scenarios where a follower vehicle interacts with a leader vehicle in one-dimensional space. However, vehicles do interact in a two-dimensional space especially in a heterogeneous traffic environment. Further, designating an interaction as risky depends on the interacting leader-follower (LF) pairs. Conflict indicators namely Time-to-Collision (TTC) and lateral gap which quantifies longitudinal and lateral interactions respectively, were computed from video recordings at four accident black spots on four-lane divided highways. Conflict in two-dimensional space was modelled for various LF-pairs using the Bivariate Extreme Value function of these two conflict indicators. Crash risk was estimated for each LF-pairs separately. Results show that cars and light commercial vehicles exhibit higher crash risk as compared to two-wheelers and motorized three-wheelers. The proposed framework can be used for more accurate risk assessment and calibration of collision warning systems in lane free mixed traffic conditions.

Analysis between Temperature and Wind Speed in East Java using Bivariate Extreme Value Theory

Extreme weather now is the biggest effect of climate change. It is also a major issue over the past decade. High heat and hurricanes are some of its indicators. Both natural disasters have a big impact not only on humans but also on the presence of animals and the environment. Therefore, modelling of the disaster, especially for prediction extreme events is the basic need to minimize the damage and the losses. Both of the hazards come from extreme temperatures and wind speeds, respectively. Hence, this paper will analyze the issues using extreme value theory (EVT) approach. We will investigate it separately and then analyze both two cases simultaneously. The results show that using peaks over threshold univariate or separately approach is the best model among other approaches since providing the smallest AIC value. Meanwhile, the value of AIC for the block maxima is smaller than peaks over threshold using the bivariate approach.

Bivariate Extreme Value Statistics of Offshore Jacket Support Stresses in Bohai Bay

This paper presents a generic Monte Carlo-based approach for bivariate extreme response prediction for fixed offshore structures, particularly jacket type. The bivariate analysis of extremes is often poorly understood and generally not adequately considered in most practical measurements/situations; that is why it is important to utilize the recently developed bivariate average conditional exceedance rate (ACER) method. According to the current literature study, there is not yet a direct application of the bivariate ACER method to coupled offshore jacket stresses. This study aims at being first to apply bivariate ACER method to jacket critical stresses, aiming at contributing to safety and reliability studies for a wide class of fixed offshore structures. An operating jacket located in the Bohai bay was taken as an example to demonstrate the proposed methodology. Satellite measured global wave statistics was used to obtain realistic wave scatter diagram in the jacket location area. Second-order wave load effects were taken into account, while simulating jacket structural response. An accurate finite element ANSYS model was used to model jacket response dynamics, subject to nonlinear hydrodynamic wave and sea current loads. Offshore structure design values are often based on univariate statistical analysis, while actually multivariate statistics is more appropriate for modeling the whole structure. This paper studies extreme stresses that are simultaneously measured/simulated at two different jacket locations. Due to less than full correlation between stresses in different critical jacket locations, application of the multivariate (or at least bivariate) extreme value theory is of practical engineering interest.

Retracted: Understanding the relationship of tourism demands connecting with economy and tourism stock index in an extreme case of Thailand bivariate extreme value copula approach

Interestingly, there is no confirmation that the Bivariate Extreme Value models and Bivariate Extreme Value Copula models are employed to explore tourism variables, especially studying in Thailand. This paper aims to statistically clarify extreme cases in tourism demands connecting with a macroeconomic level and micro tourism factor. Three quarterly indexes, including Thailand economic expansion rates, CENTEL stock indexes, and tourist arrivals were collected during 2003 to 2015. Empirically, the results showed extreme value copula models can better capture the dependence structure between three economic components than using the bivariate extreme value models. In addition, the extreme dependent results among the three comparable variables can be implied that the special tourism policies for extreme situations should not be neglected. It is reasonable to simultaneously adjusted tourism policies to both normal cases and critical situations during the whole year.

Flood Double Frequency Analysis: 2D-Archimedean Copulas vs Bivariate Probability Distributions

Floods are multidimensional phenomena which are conventionally studied considering the pairwise dependence between peak flow and flood volume or peak flow and duration. In this paper, the flood phenomenon is analysed based on the peak flow-flood volume dependence. The paper presents a comparison between two methodologies for the double frequency analysis using a bivariate probability distribution and the copulas approach. The comparison is performed with data from a case study example of the Ashuapmushuan river basin in Quebec, Canada. In the presented example the bivariate Extreme Value distribution type I (Gumbel) is used for comparison with the bivariate Gumbel-Hougaard Archimedean copula. For the parameters estimation of the the latter, the Kendall method and the maximum likelihood method are employed. Based on the derived results of the analysed example, it can be concluded that for engineering purposes, the copulas approach, regardless of the method of its parameter estimation, provides a simple and accurate approach for the frequency analysis of floods and the estimation of the design variables thereof. The Kendall estimation parameter method, as simpler method, is easier to apply.

Increased risk of heat waves in Florida: Characterizing changes in bivariate heat wave risk using extreme value analysis

Maximum and minimum daily temperatures from the second half of the 20th century are examined using a high resolution dataset of 833 grid cells across the state of Florida. A bivariate Extreme Value Analysis Point Process approach is used to model characteristics including the frequency, magnitude, duration, and timing of periods or heat waves during which both daily maximum and minimum temperatures exceed their respective 90th percentile thresholds. Variability in heat wave characteristics is examined across the state to give an indication of those areas where heat waves with certain characteristics may be more likely to occur. Changes in heat wave characteristics through time are examined by halving the temperature record and determining changes to heat wave characteristics between the two periods. This exploration of changes in heat wave risk through time gives a possible suggestion of trends in future heat wave risk. Findings indicate that there is considerable spatial variability in heat wave characteristics although heat waves have become increasingly frequent and intense throughout much of the state.

Factors Affecting Palm Oil Price Based on Extremes Value Approach

This study examines the dependence structure of extreme realization of growth rate between palm oil prices and factors affecting, which are soybean oil and crude oil prices. We employ the Bivariate Extreme Value methods for daily palm oil, soybean oil and crude oil prices ranging from July 1988 to January 2012. The results provide that the growth rate of palm oil and soybean oil prices has some dependence in extremes, but the growth rate of palm oil and crude oil prices has fairly weak dependence or even independence in extremes. Therefore, the authors of this study hoped that these findings not only have made a contribution to our understanding of what drives palm oil price movement of soybean oil and change in crude oil prices, but also for the practitioner who want to devise an updated model to enhance a further comprehension of the prices that drive these article of trade.

Testing asymptotic independence in bivariate extremes

Bivariate extreme value condition (see (1.1) below) includes the marginal extreme value conditions and the existence of the (extreme) dependence function. Two cases are of interest: asymptotic independence and asymptotic dependence. In this paper, we investigate testing the existence of the dependence function under the null hypothesis of asymptotic independence and present two suitable test statistics. Small simulations are studied and the application for a real data is shown. The other case with the null hypothesis of asymptotic dependence is already investigated.

Sobre a precisão das estimativas de máxima verossimilhança nas distribuições bivariadas de valores extremos

As distribuições bivariadas de valores extremos surgem como distribuições limites de máximos normalizados. O objetivo na modelagem do comportamento assintótico probabilístico dos extremos é obter boas aproximações para a distribuição bivariada de extremos permitindo o estudo da ocorrência de eventos extremos simultâneos. Quando trabalhamos com amostras pequenas, surgem algumas questões relacionadas à precisão e qualidade das estimativas de máxima verossimilhança dos parâmetros e de outras quantidades derivadas dos modelos bivariados de valores extremos. Neste artigo utilizamos esquemas de reamostragem bootstrap e simulações Monte Carlo para acessar a variabilidade e construir intervalos de confiança para essas estimativas, visando estabelecer o quão confiáveis são as conclusões retiradas das análises feitas com esses modelos. Valores críticos para os testes propostos por Tawn (1988) são também obtidos através de simulações.

Rates of Convergence for Bivariate Extremes

Under a second order regular variation condition, rates of convergence of the distribution of bivariate extreme order statistics to its limit distribution are given both in the total variation metric and in the uniform metric.

The extremal index for a Markov chain

The paper presents a method of computing the extremal index for a discrete-time stationary Markov chain in continuous state space. The method is based on the assumption that bivariate margins of the process are in the domain of attraction of a bivariate extreme value distribution. Scaling properties of bivariate extremes then lead to a random walk representation for the tail behaviour of the process, and hence to computation of the extremal index in terms of the fluctuation properties of that random walk. The result may then be used to determine the asymptotic distribution of extreme values from the Markov chain.

The extremal index for a Markov chain

The paper presents a method of computing the extremal index for a discrete-time stationary Markov chain in continuous state space. The method is based on the assumption that bivariate margins of the process are in the domain of attraction of a bivariate extreme value distribution. Scaling properties of bivariate extremes then lead to a random walk representation for the tail behaviour of the process, and hence to computation of the extremal index in terms of the fluctuation properties of that random walk. The result may then be used to determine the asymptotic distribution of extreme values from the Markov chain.

Regression in the Nondifferentiable Bivariate Extreme Models

Abstract This paper compares general and linear regression for the biextremal and Gumbel bivariate extreme models. The technique is based on the values of the correlation ratios and coefficients. The computations show that linear regression is a good approximation to the general one in both cases.

Regression in the Nondifferentiable Bivariate Extreme Models

Abstract This paper compares general and linear regression for the biextremal and Gumbel bivariate extreme models. The technique is based on the values of the correlation ratios and coefficients. The computations show that linear regression is a good approximation to the general one in both cases.