Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
3.5
2.4
Journals
Mathematics
Special Issues
Mathematical and Statistical Methods in Detecting and Modeling Abnormalities, Extremes,...
share announcement

Mathematical and Statistical Methods in Detecting and Modeling Abnormalities, Extremes, and Rare Events

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Probability and Statistics".

Deadline for manuscript submissions: 30 June 2024 | Viewed by 8154

Special Issue Editors

Prof. Dr. Zhengjun Zhang

E-Mail Website
Guest Editor
Department of Statistics, University of Wisconsin, Madison, WI 53706, USA
Interests: nonlinear financial time series analysis; extreme value analytics for big data; risk analysis in finance, insurance, environmental studies, and seismic data; nonlinear/asymmetric causal inference; stochastic optimization and simulation technique; hi-dimensional inference; medical informatics
Dr. Yanxi Hou

E-Mail Website
Guest Editor
School of Data Science, Fudan University, Shanghai 200433, China
Interests: extreme value theory; tail copula; quantitative risk management

Special Issue Information

Dear Colleagues,

In recent decades, various research topics have contributed to problems related to detecting abnormalities, modeling extreme values, and predicting rare events. These applications require filtering abnormal observations and exploring tail data with extremely large or small values. For instance, predicting rare weather and climate events such as heat waves, floods, and hurricanes; detecting network intrusion such as patterns of abnormal login; and estimating high-risk measures such as value-at-risk and conditional value-at-risk have constantly been drawing attention in academia, practice, and administration. Therefore, it is a significant scientific problem to develop mathematical and statistical methods to accurately establish models for extreme values or rare events from limited data.

This Special Issue aims to call for papers that present up-to-date mathematical and statistical methods for detecting and modeling abnormalities, extremes, and rare events. The scope of the applications includes but is not restricted to climate and atmospheric science, risk management, reliability, geosciences, hydrology, finance, economics, insurance, neuroscience, rare diseases, and epidemiology. In addition, theoretical and empirical studies with new methodologies are welcome in the presence of abnormalities, extremes, and rare events.

Prof. Dr. Zhengjun Zhang
Dr. Yanxi Hou
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • extreme value theory
  • risk analysis
  • applications
  • tail uncertainty and causality quantifications

Published Papers (5 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

24 pages, 5333 KiB  
Article
Analysis of Probability Distributions for Modelling Extreme Rainfall Events and Detecting Climate Change: Insights from Mathematical and Statistical Methods
by Raúl Montes-Pajuelo, Ángel M. Rodríguez-Pérez, Raúl López and César A. Rodríguez
Mathematics 2024, 12(7), 1093; https://doi.org/10.3390/math12071093 - 4 Apr 2024
Viewed by 798
Abstract
Exploring the realm of extreme weather events is indispensable for various engineering disciplines and plays a pivotal role in understanding climate change phenomena. In this study, we examine the ability of 10 probability distribution functions—including exponential, normal, two- and three-parameter log-normal, gamma, Gumbel, [...] Read more.
Exploring the realm of extreme weather events is indispensable for various engineering disciplines and plays a pivotal role in understanding climate change phenomena. In this study, we examine the ability of 10 probability distribution functions—including exponential, normal, two- and three-parameter log-normal, gamma, Gumbel, log-Gumbel, Pearson type III, log-Pearson type III, and SQRT-ET max distributions—to assess annual maximum 24 h rainfall series obtained over a long period (1972–2022) from three nearby meteorological stations. Goodness-of-fit analyses including Kolmogorov–Smirnov and chi-square tests reveal the inadequacy of exponential and normal distributions in capturing the complexity of the data sets. Subsequent frequency analysis and multi-criteria assessment enable us to discern optimal functions for various scenarios, including hydraulic engineering and sediment yield estimation. Notably, the log-Gumbel and three-parameter log-normal distributions exhibit superior performance for high return periods, while the Gumbel and three-parameter log-normal distributions excel for lower return periods. However, caution is advised regarding the overuse of log-Gumbel, due to its high sensitivity. Moreover, as our study considers the application of mathematical and statistical methods for the detection of extreme events, it also provides insights into climate change indicators, highlighting trends in the probability distribution of annual maximum 24 h rainfall. As a novelty in the field of functional analysis, the log-Gumbel distribution with a finite sample size is utilised for the assessment of extreme events, for which no previous work seems to have been conducted. These findings offer critical perspectives on extreme rainfall modelling and the impacts of climate change, enabling informed decision making for sustainable development and resilience. Full article
(This article belongs to the Special Issue Mathematical and Statistical Methods in Detecting and Modeling Abnormalities, Extremes, and Rare Events)
►▼ Show Figures

Figure 1

32 pages, 3118 KiB  
Article
Tail Risk Signal Detection through a Novel EGB2 Option Pricing Model
by Hang Lin, Lixin Liu and Zhengjun Zhang
Mathematics 2023, 11(14), 3194; https://doi.org/10.3390/math11143194 - 20 Jul 2023
Viewed by 1874
Abstract
Connecting derivative pricing with tail risk management has become urgent for financial practice and academia. This paper proposes a novel option pricing model based on the exponential generalized beta of the second kind (EGB2) distribution. The newly proposed model is of generality, simplicity, [...] Read more.
Connecting derivative pricing with tail risk management has become urgent for financial practice and academia. This paper proposes a novel option pricing model based on the exponential generalized beta of the second kind (EGB2) distribution. The newly proposed model is of generality, simplicity, robustness, and financial interpretability. Most importantly, one can detect tail risk signals by calibrating the proposed model. The model includes the seminal Black–Scholes (B−S) formula as a limit case and can perfectly “replicate” the option prices from Merton’s jump-diffusion model. Based on the proposed pricing model, three tail risk warning measures are introduced for tail risk signals detection: the EGB2 implied tail index, the EGB2 implied Value-at-Risk (EGB2-VaR), and the EGB2 implied risk-neutral density (EGB2 R.N.D.). Empirical results show that the new pricing model can yield higher pricing accuracy than existing models in normal and crisis periods, and three model-based tail risk measures can perfectly detect tail risk signals before financial crises. Full article
(This article belongs to the Special Issue Mathematical and Statistical Methods in Detecting and Modeling Abnormalities, Extremes, and Rare Events)
►▼ Show Figures

Figure 1

14 pages, 871 KiB  
Article
Extremal Analysis of Flooding Risk and Its Catastrophe Bond Pricing
by Jiayi Li, Zhiyan Cai, Yixuan Liu and Chengxiu Ling
Mathematics 2023, 11(1), 114; https://doi.org/10.3390/math11010114 - 27 Dec 2022
Cited by 3 | Viewed by 1886
Abstract
Catastrophic losses induced by natural disasters are receiving growing attention because of the severe increases in their magnitude and frequency. We first investigated the extreme tail behavior of flood-caused economic losses and maximum point precipitation based on the peaks-over-threshold method and point process [...] Read more.
Catastrophic losses induced by natural disasters are receiving growing attention because of the severe increases in their magnitude and frequency. We first investigated the extreme tail behavior of flood-caused economic losses and maximum point precipitation based on the peaks-over-threshold method and point process (PP) model and its extreme tail dependence. We found that both maximum point precipitation and direct economic losses are well-modeled by the PP approach with certain tail dependence. These findings were further utilized to design a layered compensation insurance scheme using estimated value-at-risk (VaR) and conditional VaR (CVaR) among all stakeholders. To diversify the higher level of losses due to extreme precipitation, we designed a coupon paying catastrophe bond triggered by hierarchical maximum point precipitation level, based on the mild assumption on the independence between flood-caused risk and financial risk. The pricing sensitivity was quantitatively analyzed in terms of the tail risk of the flood disaster and the distortion magnitude and the market risk in Wang’s transform. Our trigger process was carefully designed using a compound Poisson process, modeling both the frequency and the layered intensity of flood disasters. Lastly, regulations and practical suggestions are provided regarding the flood risk prevention and warning. Full article
(This article belongs to the Special Issue Mathematical and Statistical Methods in Detecting and Modeling Abnormalities, Extremes, and Rare Events)
►▼ Show Figures

Figure 1

11 pages, 268 KiB  
Article
Point Processes in a Metric Space and Their Applications
by Yuwei Zhao
Mathematics 2022, 10(21), 4002; https://doi.org/10.3390/math10214002 - 28 Oct 2022
Viewed by 691
Abstract
Point processes are important in extreme value theory due to their equivalent formulations of two popular models in various applications: the block maxima models and the peak-over-threshold model. Point processes in a metric space provide tools to analyze heavy-tailed phenomena that appear in [...] Read more.
Point processes are important in extreme value theory due to their equivalent formulations of two popular models in various applications: the block maxima models and the peak-over-threshold model. Point processes in a metric space provide tools to analyze heavy-tailed phenomena that appear in the research of extremal behaviors of functional data. To facilitate these applications of point processes, the equivalence between the weak convergence of point processes and the MO-convergence is established in the paper. Full article
(This article belongs to the Special Issue Mathematical and Statistical Methods in Detecting and Modeling Abnormalities, Extremes, and Rare Events)
22 pages, 3552 KiB  
Article
A Versatile and Efficient Novel Approach for Mendelian Randomization Analysis with Application to Assess the Causal Effect of Fetal Hemoglobin on Anemia in Sickle Cell Anemia
by Janaka S. S. Liyanage, Jeremie H. Estepp, Kumar Srivastava, Sara R. Rashkin, Vivien A. Sheehan, Jane S. Hankins, Clifford M. Takemoto, Yun Li, Yuehua Cui, Motomi Mori, Stephen Burgess, Michael R. DeBaun and Guolian Kang
Mathematics 2022, 10(20), 3743; https://doi.org/10.3390/math10203743 - 12 Oct 2022
Cited by 1 | Viewed by 1938
Abstract
Mendelian randomization (MR) is increasingly employed as a technique to assess the causation of a risk factor on an outcome using observational data. The two-stage least-squares (2SLS) procedure is commonly used to examine the causation using genetic variants as the instrument variables. The [...] Read more.
Mendelian randomization (MR) is increasingly employed as a technique to assess the causation of a risk factor on an outcome using observational data. The two-stage least-squares (2SLS) procedure is commonly used to examine the causation using genetic variants as the instrument variables. The validity of 2SLS relies on a representative sample randomly selected from a study cohort or a population for genome-wide association study (GWAS), which is not always true in practice. For example, the extreme phenotype sequencing (EPS) design is widely used to investigate genetic determinants of an outcome in GWAS as it bears many advantages such as efficiency, low sequencing or genotyping cost, and large power in detecting the involvement of rare genetic variants in disease etiology. In this paper, we develop a novel, versatile, and efficient approach, namely MR analysis under Extreme or random Phenotype Sampling (MREPS), for one-sample MR analysis based on samples drawn through either the random sampling design or the nonrandom EPS design. In simulations, MREPS provides unbiased estimates for causal effects, correct type I errors for causal effect testing. Furthermore, it is robust under different study designs and has high power. These results demonstrate the superiority of MREPS over the widely used standard 2SLS approach. We applied MREPS to assess and highlight the causal effect of total fetal hemoglobin on anemia risk in patients with sickle cell anemia using two independent cohort studies. A user-friendly Shiny app web interface was implemented for professionals to easily explore the MREPS. Full article
(This article belongs to the Special Issue Mathematical and Statistical Methods in Detecting and Modeling Abnormalities, Extremes, and Rare Events)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-5
Back to TopTop