Article
Engineering, Marine
Ross Towe, David Randell, Jennifer Kensler, Graham Feld, Philip Jonathan
Summary: The design and reanalysis of offshore and coastal structures often involves estimating return values and associated values for metocean variables using extreme value analysis. This study examines different estimation methods for these values, taking into account sampling uncertainty. The results of a simulation experiment show that certain estimators perform better than others, and that models incorporating appropriate descriptions of marginal and dependence provide more accurate estimates. The study also suggests that probabilistic risk analysis incorporating full uncertainty propagation is preferable to summarising joint tail characteristics of metocean variables.
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)
Review
Mathematics
Natalia Markovich, Marijus Vaiciulis
Summary: This paper summarizes recent research results on the evolution of random networks and related extreme value statistics, which are of great interest due to their numerous applications. The focus is on the statistical methodology rather than the structure of random networks. The problems arising in evolving networks, particularly due to the heavy-tailed nature of node indices, are discussed. Topics such as tail and extremal indices, preferential and clustering attachments, community detection, stationarity and dependence of graphs, information spreading, and finding influential leading nodes and communities are surveyed. The paper aims to propose possible solutions to unsolved problems and provides a comprehensive review of estimators for tail and extremal indices on random graphs.
Article
Environmental Sciences
S. Basso, G. Botter, R. Merz, A. Miniussi
Summary: The study highlights the physically-based alternative distribution PHEV for predicting flood magnitude and frequency, which has better predictive capabilities compared to statistical methods, especially for rare floods. The analysis results demonstrate the applicability of PHEV to long time series and observational datasets in various hydro-climatic regions, with reduced prediction uncertainty in estimating flood magnitudes.
ENVIRONMENTAL RESEARCH LETTERS
(2021)
Article
Geochemistry & Geophysics
Ziheng Xia, Penghui Wang, Ganggang Dong, Hongwei Liu
Summary: Radar automatic target recognition (RATR) using high-resolution range profiles (HRRP) has gained attention, but previous works primarily focus on closed set recognition and may lead to errors in open set environments. This article proposes open set recognition to address this issue by establishing a closed classification boundary. The proposed extreme value boundary theorem demonstrates that the maximum distance from known features to the cluster center follows a generalized extreme value distribution, enabling the determination of a closed classification boundary to distinguish between known and unknown classes. Extensive experiments on measured HRRP data validate the proposed theorem and method.
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
(2023)
Article
Environmental Sciences
Shailza Sharma, P. P. Mujumdar
Summary: This study investigates the suitability of parametric multivariate extreme value models to correctly represent and estimate the dependence structure of concurrent extremes. The results demonstrate the ability of parametric multivariate models to characterize the complex dependence structure of concurrent extremes.
WATER RESOURCES RESEARCH
(2022)
Article
Meteorology & Atmospheric Sciences
Marc-Andre Falkensteiner, Harald Schellander, Gregor Ehrensperger, Tobias Hell
Summary: This paper proposes a modification of the MEVD method, called TMEV, for the analysis of non-stationary precipitation extremes. The TMEV method can explicitly account for seasonal differences and identify longterm trends and seasonal variations. Experimental results show that the TMEV method provides similar error characteristics to the simplified MEVD method for estimating quantiles.
WEATHER AND CLIMATE EXTREMES
(2023)
Article
Water Resources
Cuauhtemoc Tonatiuh Vidrio-Sahagun, Jianxun He, Alain Pietroniro
Summary: The nonstationary hydrological frequency analysis (NS-HFA) plays an important role in evaluating the recurrence of hydrological extremes under nonstationarity. The Metastatistical extreme value (MEV) distribution has been widely used under stationarity and limited record lengths. However, its nonstationary applications are lacking. This paper develops a nonstationary MEV-based model for NS-HFA, which outperforms other benchmark models in terms of uncertainty, accuracy, and fitting efficiency.
ADVANCES IN WATER RESOURCES
(2023)
Article
Statistics & Probability
Holger Drees
Summary: The extreme value dependence of independent variables is analyzed in this study. Estimators for the spectral measure at a specific time point and the integrated spectral measure are proposed. The uniform asymptotic normality of these estimators is proved under appropriate nonparametric smoothness and regularity assumptions. Consistent tests for the null hypothesis that the spectral measure does not change over time are then developed based on the process convergence of the integrated spectral measure.
ANNALS OF STATISTICS
(2023)
Article
Economics
Chandra R. Bhat
Summary: In this paper, a new two-stage budgeting-based utility-theoretic econometric multiple discrete-count model is proposed by linking a fractional split MDCEV model component with a total count model. By specifying error distributions in the model, a multiple discrete-count extreme value (MDCNTEV) model with a closed-form probability expression is derived and estimated using maximum likelihood estimation. An application of the proposed model is demonstrated in the context of individuals' multivariate count of recreational episodes to multiple possible tourism destination locations, showing the potential of the model in various multivariate count consumer choice settings.
TRANSPORTATION RESEARCH PART B-METHODOLOGICAL
(2022)
Article
Computer Science, Interdisciplinary Applications
Tzong-Ru Tsai, Chia-Min Hung, Y. L. Lio, Jyun-You Chiang, H. K. T. Ng
Summary: This study introduces a novel quality control method to monitor the relationship between response and auxiliary variables using the smallest extreme value distributions model, proposing a new control chart approach. Compared to competitors, this control chart is more reliable in terms of false alarm rate.
JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION
(2022)
Article
Mathematics
Xi Liu, Yiqiao Jin, Yifan Yang, Xiaoqing Pan
Summary: This paper investigates the marginal and conditional distributions of a multivariate folded normal distribution and proves the equivalence of independence and non-correlation for it. A numerical approach using the R language is also presented to fit the distribution, with an examination of the accuracy of the estimated mean and variance parameters. Lastly, a real data application on body mass index is provided.
Article
Multidisciplinary Sciences
Raul Alejandro Moran-Vasquez, Alejandro Roldan-Correa, Daya K. Nagar
Summary: We propose a new multivariate skewed distribution with positive support, called the quantile-based multivariate log-normal distribution, which has interpretable parameters in terms of marginal quantiles and associations between variables. We derive various statistical properties of this distribution, such as transformations, mixed moments, expected value, covariance matrix, mode, Shannon entropy, and Kullback-Leibler divergence. We also discuss parameter estimation and evaluate the model fitting using Mahalanobis-type distances, with an application to children data.
Article
Engineering, Mechanical
Jinhua Li, Desen Zhu, Liyuan Cao, Chunxiang Li
Summary: This study proposes a novel simplified wavelet transform-based stationary transformation method (PNGEV) for extreme value analysis. The effectiveness and practicality of the PNGEV method are verified through comparisons with the traditional method (TNGEV).
PROBABILISTIC ENGINEERING MECHANICS
(2023)
Article
Computer Science, Information Systems
Rumaisa Kruba, Muhammad Mashuri, Dedy Dwi Prastyo
Summary: The study introduces a new control chart, Max-Half-Mchart, which uses a half-normal distribution to improve process control performance. Results show that Max-Half-Mchart outperforms Max-Mchart in terms of Average Run Length (ARL) and real data scenarios, and is consistent with statistics in other control charts.
Article
Statistics & Probability
Alexander Iksanov, Zakhar Kabluchko, Alexander Marynych
ELECTRONIC JOURNAL OF PROBABILITY
(2016)
Article
Statistics & Probability
Alexander Iksanov, Zakhar Kabluchko, Alexander Marynych
STATISTICS & PROBABILITY LETTERS
(2016)
Article
Mathematics
Zakhar Kabluchko, Dmitry Zaporozhets
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2016)
Article
Statistics & Probability
Alexander Iksanov, Zakhar Kabluchko, Alexander Marynych, Georgiy Shevchenko
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2017)
Article
Statistics & Probability
Clement Dombry, Zakhar Kabluchko
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2017)
Article
Statistics & Probability
Hendrik Flasche, Zakhar Kabluchko
JOURNAL OF THEORETICAL PROBABILITY
(2020)
Article
Computer Science, Theory & Methods
Zakhar Kabluchko
Summary: The study investigates the probability distribution of random simplices and their internal angles in n-dimensional space, as well as related calculations based on beta density.
DISCRETE & COMPUTATIONAL GEOMETRY
(2021)
Article
Mathematics
Zakhar Kabluchko
Summary: This paper discusses the expected f-vectors of random beta and random beta' polytopes, and derives alternative formulas through algebraic manipulations. Additionally, it explores the algebraic properties of Stirling numbers.
BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY
(2023)
Article
Statistics & Probability
Zakhar Kabluchko, Alexander Marynych
Summary: This paper studies the probability of k-neighborliness in the polytope C-n,C-d in various high-dimensional asymptotic regimes. By introducing the Lah distribution and computing its factorial moments, the neighborliness properties of the polytope are demonstrated.
PROBABILITY THEORY AND RELATED FIELDS
(2022)
Article
Statistics & Probability
Thomas Godland, Zakhar Kabluchko
Summary: We study random convex cones defined as positive hulls of d-dimensional random walks and bridges and compute expectations of various geometric functionals of these cones.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2022)
Article
Mathematics, Applied
Thomas Godland, Zakhar Kabluchko
Summary: This paper studies a belt polytope P with a hyperplane arrangement, and the effect of a linear map G on the number of faces of P under projection. The research shows that the number of faces of the projected polytope GP is related to the j-th level characteristic polynomial of the hyperplane arrangement, regardless of the linear map G. In addition, the research also provides formulas for calculating the sum of the conic intrinsic volumes and Grassmann angles of the tangent cones of P at all its j-faces. Finally, the research applied to permutohedra of types A and B, deriving closed formulas for the face numbers of projected permutohedra and the generalized angle sums of permutohedra in terms of Stirling numbers and their B-analogues.
RESULTS IN MATHEMATICS
(2023)
Article
Computer Science, Theory & Methods
Zakhar Kabluchko
Summary: This article examines the properties of metric projections of points onto chambers in a hyperplane arrangement and proves the relationship between the dimension of the metric projection and the coefficients of the characteristic polynomial of the hyperplane arrangement.
DISCRETE & COMPUTATIONAL GEOMETRY
(2023)
Article
Statistics & Probability
Thomas Godland, Zakhar Kabluchko
Summary: A new direct proof for the conic intrinsic volumes formulas of the Weyl chambers of types A(n-1), B-n, and D-n is presented in this article. The formulas are expressed in terms of the Stirling numbers of the first kind and their B- and D-analogues. The proof involves the explicit determination of the internal and external angles of the faces of the Weyl chambers.
MODERN STOCHASTICS-THEORY AND APPLICATIONS
(2022)
Article
Computer Science, Theory & Methods
Zakhar Kabluchko, Guenter Last, Dmitry Zaporozhets
DISCRETE & COMPUTATIONAL GEOMETRY
(2017)
