Article
Engineering, Marine
Xiaoyu Zhou, Hongxia Li, Yi Huang, Yihua Liu
Summary: This study proposes a new extreme statistics strategy to predict the extreme parametric rolling angle with minimal model test observations. The strategy utilizes a synthetic moment method based on the Hermite transformation and Markov chain to predict extreme values for stationary processes. A specific simplification technique is also introduced to address the non-stationarity issue of parametric roll. By applying the new strategy, the CDF and PDF of the extreme parametric rolling angle for the C11 container ship are obtained from only one observed model test time history. The validity of these predictions is verified through data statistics of other model tests and numerous numerical simulations.
Article
Statistics & Probability
Laurens de Haan, Chen Zhou
Summary: This study explores extreme value analysis for independent but nonidentically distributed observations, providing a nonparametric estimate for the functional extreme value index. In addition to locally estimating the extreme value index, a global estimator for the trend and its joint asymptotic theory are also offered for testing a prespecified parametric trend in the extreme value indices. It can be applied to test whether the extreme value index remains at a constant level across all observations.
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
(2021)
Article
Acoustics
Zhao Zhao, Ying Min Low
Summary: This study presents an analytical method for extreme analysis of multivariate stationary Gaussian processes, which efficiently solves high-dimensional problems and has diverse applications. By defining a maximum process and utilizing the Poisson approximation method to estimate extreme value distribution, the method ensures fast computation.
JOURNAL OF SOUND AND VIBRATION
(2023)
Article
Physics, Fluids & Plasmas
Prashant Singh
Summary: In this paper, we study a simple model of heterogeneous diffusion with a power-law varying diffusion coefficient. We derive the probability distributions of the maximum spatial displacement and arg-maximum time for all values of the power-law exponent. We also analyze the statistical properties of the residence time and the last-passage time and calculate their distributions exactly. Our study reveals that the heterogeneous version displays contrasting features compared to standard Brownian motion.
Article
Engineering, Marine
Connor J. McCluskey, Manton J. Guers, Stephen C. Conlon
Summary: Extreme value statistics is a method for determining maximum design loads in extreme conditions, with accurate predictions requiring large sample sizes and small sample sizes leading to greater variation. The proposed method estimates minimum sample sizes by obtaining an acceptable variance for extreme value processes and is designed for use with various distribution behaviors.
Article
Statistics & Probability
John H. J. Einmahl, Yi He
Summary: We extend extreme value statistics to independent data with possibly very different distributions. In particular, we present novel asymptotic normality results for the Hill estimator, which estimates the extreme value index of the average distribution. Due to heterogeneity, the asymptotic variance can be substantially smaller than that in the i.i.d. case. We also present applications to assess the tail heaviness of earthquake energies and of cross-sectional stock market losses.
ANNALS OF STATISTICS
(2023)
Article
Mechanics
Alessandro Taloni, Stefano Zapperi
Summary: The fracture stress of materials typically depends on sample size and is traditionally explained using extreme value statistics. A recent study interpreted the carrying capacity of long polyamide and polyester wires in terms of a probabilistic argument called the St. Petersburg paradox, but the same results can be better explained using extreme value statistics. The relevance of rate dependent effects was also discussed.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2021)
Article
Computer Science, Interdisciplinary Applications
Zeng Meng, Jingyu Zhao, Chen Jiang
Summary: This paper proposes a semi-analytical extreme value method, which transforms the time-variant performance function into instantaneous performance functions, approximates each instantaneous function by Taylor series expansion at the most probable point through instantaneous reliability analysis, significantly reducing the computational cost of the extreme value method.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Mathematics
Jorge Castillo-Mateo, Jesus Asin, Ana C. Cebrian, Jesus Mateo-Lazaro, Jesus Abaurrea
Summary: In many applications, there is a need to assess relationships between covariates and extreme values of a continuous response. A Bayesian method for variable selection based on a stochastic search algorithm is proposed to address the issue in moderately high dimensional variable selection in GEV regression. The method is applied to select atmospheric covariates in annual maximum temperature series in three Spanish stations.
Article
Mathematics, Interdisciplinary Applications
Wu Fan, Kong Xinbing, Xu Chao
Summary: In this paper, the authors introduce a new sequential testing procedure for obtaining a consistent estimator of the number of communities based on locally smoothed adjacency matrix and extreme value theory. The method is simple, with high detection power, and serves as an alternative approach to random matrix theory in Lei (2016). Additionally, a two-sample test for the stochastic block model with two observed adjacency matrices is proposed for detecting changes in community structure, with simulation studies supporting the theory.
JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
(2022)
Article
Materials Science, Multidisciplinary
Krzysztof S. S. Stopka, Mohammadreza Yaghoobi, John E. E. Allison, David L. L. McDowell
Summary: Assessing the size of representative volume elements (RVEs) for fatigue-related applications is challenging. The present study aims to systematically investigate the trends of convergence in the simulated distribution of driving force for fatigue crack formation as a function of the size of a statistical sample of microstructure. The results show that the simulated RVE of polycrystalline microstructure using crystal plasticity finite element method converges with tens of thousands of grains, while larger volumes are required for random and rolled textures.
Article
Economics
Yuki Oyama, Yusuke Hara, Takashi Akamatsu
Summary: This study fills the research gap by establishing a Markovian traffic equilibrium assignment based on the network generalized extreme value (NGEV) model. The study provides the necessary theoretical developments for the NGEV equilibrium assignment, including the formulation and solution under the same path algebra as traditional models. Equivalent optimization formulations are also presented, allowing for efficient solution algorithms. The numerical experiments demonstrate the excellent convergence and complementary relationship of the proposed algorithms.
TRANSPORTATION RESEARCH PART B-METHODOLOGICAL
(2022)
Article
Mathematics, Applied
Sean D. Lawley
Summary: The paper investigates the distribution of extreme first passage times of piecewise deterministic Markov processes (PDMPs) by using classical extreme value theory to prove general theorems for the distribution and moments of extreme FPTs in the limit of many searchers. The results are then applied to canonical PDMPs, including run and tumble searchers in different dimensions, and discussed in the context of biological systems. The approach also addresses an unphysical property of diffusion that can be problematic for extreme statistics.
Article
Statistics & Probability
Lanpeng Ji, Xiaofan Peng
Summary: We investigate the extreme value theory of a class of random sequences defined by the all-time suprema of aggregated self-similar Gaussian processes with trend. This study is motivated by its potential applications in various areas and its theoretical interestingness. We consider both stationary and non-stationary sequences and show that suitably normalized kth order statistics converge in distribution to a limiting random variable, which can be a negative log transformed Erlang distributed random variable, a Normal random variable, or a mixture of them.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2023)
Article
Engineering, Mechanical
Adrienne Muth, Reji John, Adam Pilchak, Surya R. Kalidindi, David L. McDowell
Summary: This study utilizes extreme value statistics to model Fatigue Indicator Parameters, capturing fatigue crack formation mechanisms and early growth stages to evaluate resistance to fatigue in Ti-6Al-4V microstructures. The statistical volume element ensemble approach and peaks-over-threshold method are used to rank microstructures based on their resistance to fatigue crack formation. Microstructure attributes such as grain size, orientation, and nearest neighbor arrangements are quantified in FIP 'hot spots'.
INTERNATIONAL JOURNAL OF FATIGUE
(2021)
