Asymptotic expansion for distribution function of the moment estimator $\hat \gamma _n^M $ for the extreme-value index is obtained under reasonable conditions of second order regular variation.
Let M_(n,p)=(X_(i,k))_(n×p)be an n×p random matrix whose p columns X^((1)),...,X^((p))are an n-dimensional i.i.d.random sample of size p from 1-dependent Gaussian populations.Instead of investigating the spe...Let M_(n,p)=(X_(i,k))_(n×p)be an n×p random matrix whose p columns X^((1)),...,X^((p))are an n-dimensional i.i.d.random sample of size p from 1-dependent Gaussian populations.Instead of investigating the special case where p and n are comparable,we consider a much more general case in which log n=o(p^(1/3)).We prove that the maximum interpoint distance Mn=max{|X_(i)-X_(j)|;1≤i<j≤n}converges to an extreme-value distribution,where X_(i)and X_(j)denote the i-th and j-th row of M_(n,p),respectively.The proofs are completed by using the Chen-Stein Poisson approximation method and the moderation deviation principle.展开更多
Universality,encompassing critical exponents,scaling functions,and dimensionless quantities,is fundamental to phase transition theory.In finite systems,universal behaviors are also expected to emerge at the pseudocrit...Universality,encompassing critical exponents,scaling functions,and dimensionless quantities,is fundamental to phase transition theory.In finite systems,universal behaviors are also expected to emerge at the pseudocritical point.Focusing on two-dimensional percolation,we show that the size distribution of the largest cluster asymptotically approaches to a Gumbel form in the subcritical phase,a Gaussian form in the supercritical phase,and transitions within the critical finite-size scaling window.Numerical results indicate that,at consistently defined pseudocritical points,this distribution exhibits a universal form across various lattices and percolation models(bond or site),within error bars,yet differs from the distribution at the critical point.The critical polynomial,universally zero for two-dimensional percolation at the critical point,becomes nonzero at pseudocritical points.Nevertheless,numerical evidence suggests that the critical polynomial,along with other dimensionless quantities such as wrapping probabilities and Binder cumulants,assumes fixed values at the pseudocritical point that are independent of the percolation type(bond or site)but vary with lattice structures.These findings imply that while strict universality breaks down at the pseudocritical point,certain extreme-value statistics and dimensionless quantities exhibit quasi-universality,revealing a subtle connection between scaling behaviors at critical and pseudocritical points.展开更多
With the aim to the quantification of anomaly identification and extraction for observed or analyzed records, we present two statistical methods of earthquake corresponding relevancy spectrum （ECRS） and sliding mean...With the aim to the quantification of anomaly identification and extraction for observed or analyzed records, we present two statistical methods of earthquake corresponding relevancy spectrum （ECRS） and sliding mean relevancy （SMR）. With ECRS method, we can obtain the abnormal confidence attribute of data in different value ranges. Based on the relevancy spectrum in different studied time-intervals, we convert the original time sequence into relevancy time sequence, and can obtain the SMR time series by using the multi-point cumulative sliding mean method. Then we can identify the seismic precursor anomaly. We test this method by taking the time sequence of r/-value in the northern Tianshan region as original data. The result shows that when the studied time-interval is 18 months, the precursor anomaly can be identified bet- ter from sliding mean relevancy. The anomaly corresponding rate is 83 percent, the earthquake corresponding rate is 86 per- cent, and the anomaly is characteristic of the middle term. To try the research on multi-parameter comprehensive application, we take the Kalpin tectonic block in Xinjiang as our studied region, and analyze the spatial and temporal abnormal characters of multi-parameter sliding extreme-value relevancy （MSER） before mid-strong earthquakes in the Kalpin block. The result indicates that ECRS and SMR sequence in different time-intervals can not only be used to identify the precursor anomaly of single-item data, but also offer the data of quantitative single-item anomaly for comprehensive earthquake analysis and prediction.展开更多
A changepoint in statistical applications refers to an observational time point at which the structure pattern changes during a somewhat long-term experimentation process. In many cases, the change point time and caus...A changepoint in statistical applications refers to an observational time point at which the structure pattern changes during a somewhat long-term experimentation process. In many cases, the change point time and cause are documented and it is reasonably straightforward to statistically adjust (homogenize) the series for the effects of the changepoint. Sadly many changepoint times are undocumented and the changepoint times themselves are the main purpose of study. In this article, the changepoint analysis in two-phrase linear regression models is developed and discussed. Following Liu and Qian (2010)'s idea in the segmented linear regression models, the modified empirical likelihood ratio statistic is proposed to test if there exists a changepoint during the long-term experiment and observation. The modified empirical likelihood ratio statistic is computation-friendly and its ρ-value can be easily approximated based on the large sample properties. The procedure is applied to the Old Faithful geyser eruption data in October 1980.展开更多
In this study, fatigue tests under different R ratios were conducted on the AZ61 Mg alloy to investigate its fatigue lifetimes and fatigue crack growth (FCG) behavior. The fracture surface of the failed specimens was ...In this study, fatigue tests under different R ratios were conducted on the AZ61 Mg alloy to investigate its fatigue lifetimes and fatigue crack growth (FCG) behavior. The fracture surface of the failed specimens was investigated using a scanning electron microscope to study the size of the intermetallic compounds from which the pioneer fatigue crack initiated and led to the final failure of the specimen. To determine the maximum size of the intermetallic compounds existing within the cross section of the specimen at higher risk, Gumbel’s extreme-value statistics were utilized. In the present study, the intermetallic compounds contained within the specimen were assumed to be the initial cracks existing in the material before the fatigue tests. A modified linear elastic fracture-mechanics parameter, M, proposed by McEvily et al., was used to analyze the short FCG behavior under different stress ratios, R. The relation between the rate of FCG and M parameter was found to be useful and appropriate for predicting the fatigue lifetimes under different R ratios. Moreover, the probabilistic stress-fatigue life (P-S-N) curve of the material under different R ratios could be predicted with this method, which utilizes both the FCG law and a statistical distribution of sizes of the most dangerous intermetallic compounds. The evaluated results were in good agreement with the experimental ones. This correspondence indicates that the estimation method proposed in the present study is effective for evaluation of the probabilistic stress-fatigue life (P-S-N) curve of the material under different R ratios.展开更多
文摘Asymptotic expansion for distribution function of the moment estimator $\hat \gamma _n^M $ for the extreme-value index is obtained under reasonable conditions of second order regular variation.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1177117812171198)+2 种基金the Science and Technology Development Program of Jilin Province(Grant No.20210101467JC)the Technology Program of Jilin Educational Department During the“14th Five-Year”Plan Period(Grant No.JJKH20241239KJ)the Fundamental Research Funds for the Central Universities.
文摘Let M_(n,p)=(X_(i,k))_(n×p)be an n×p random matrix whose p columns X^((1)),...,X^((p))are an n-dimensional i.i.d.random sample of size p from 1-dependent Gaussian populations.Instead of investigating the special case where p and n are comparable,we consider a much more general case in which log n=o(p^(1/3)).We prove that the maximum interpoint distance Mn=max{|X_(i)-X_(j)|;1≤i<j≤n}converges to an extreme-value distribution,where X_(i)and X_(j)denote the i-th and j-th row of M_(n,p),respectively.The proofs are completed by using the Chen-Stein Poisson approximation method and the moderation deviation principle.
基金supported by the National Natural Science Foundation of China(Grant No.12275263)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0301900)Natural Science Foundation of Fujian Province of China(Grant No.2023J02032).
文摘Universality,encompassing critical exponents,scaling functions,and dimensionless quantities,is fundamental to phase transition theory.In finite systems,universal behaviors are also expected to emerge at the pseudocritical point.Focusing on two-dimensional percolation,we show that the size distribution of the largest cluster asymptotically approaches to a Gumbel form in the subcritical phase,a Gaussian form in the supercritical phase,and transitions within the critical finite-size scaling window.Numerical results indicate that,at consistently defined pseudocritical points,this distribution exhibits a universal form across various lattices and percolation models(bond or site),within error bars,yet differs from the distribution at the critical point.The critical polynomial,universally zero for two-dimensional percolation at the critical point,becomes nonzero at pseudocritical points.Nevertheless,numerical evidence suggests that the critical polynomial,along with other dimensionless quantities such as wrapping probabilities and Binder cumulants,assumes fixed values at the pseudocritical point that are independent of the percolation type(bond or site)but vary with lattice structures.These findings imply that while strict universality breaks down at the pseudocritical point,certain extreme-value statistics and dimensionless quantities exhibit quasi-universality,revealing a subtle connection between scaling behaviors at critical and pseudocritical points.
文摘With the aim to the quantification of anomaly identification and extraction for observed or analyzed records, we present two statistical methods of earthquake corresponding relevancy spectrum （ECRS） and sliding mean relevancy （SMR）. With ECRS method, we can obtain the abnormal confidence attribute of data in different value ranges. Based on the relevancy spectrum in different studied time-intervals, we convert the original time sequence into relevancy time sequence, and can obtain the SMR time series by using the multi-point cumulative sliding mean method. Then we can identify the seismic precursor anomaly. We test this method by taking the time sequence of r/-value in the northern Tianshan region as original data. The result shows that when the studied time-interval is 18 months, the precursor anomaly can be identified bet- ter from sliding mean relevancy. The anomaly corresponding rate is 83 percent, the earthquake corresponding rate is 86 per- cent, and the anomaly is characteristic of the middle term. To try the research on multi-parameter comprehensive application, we take the Kalpin tectonic block in Xinjiang as our studied region, and analyze the spatial and temporal abnormal characters of multi-parameter sliding extreme-value relevancy （MSER） before mid-strong earthquakes in the Kalpin block. The result indicates that ECRS and SMR sequence in different time-intervals can not only be used to identify the precursor anomaly of single-item data, but also offer the data of quantitative single-item anomaly for comprehensive earthquake analysis and prediction.
文摘A changepoint in statistical applications refers to an observational time point at which the structure pattern changes during a somewhat long-term experimentation process. In many cases, the change point time and cause are documented and it is reasonably straightforward to statistically adjust (homogenize) the series for the effects of the changepoint. Sadly many changepoint times are undocumented and the changepoint times themselves are the main purpose of study. In this article, the changepoint analysis in two-phrase linear regression models is developed and discussed. Following Liu and Qian (2010)'s idea in the segmented linear regression models, the modified empirical likelihood ratio statistic is proposed to test if there exists a changepoint during the long-term experiment and observation. The modified empirical likelihood ratio statistic is computation-friendly and its ρ-value can be easily approximated based on the large sample properties. The procedure is applied to the Old Faithful geyser eruption data in October 1980.
文摘In this study, fatigue tests under different R ratios were conducted on the AZ61 Mg alloy to investigate its fatigue lifetimes and fatigue crack growth (FCG) behavior. The fracture surface of the failed specimens was investigated using a scanning electron microscope to study the size of the intermetallic compounds from which the pioneer fatigue crack initiated and led to the final failure of the specimen. To determine the maximum size of the intermetallic compounds existing within the cross section of the specimen at higher risk, Gumbel’s extreme-value statistics were utilized. In the present study, the intermetallic compounds contained within the specimen were assumed to be the initial cracks existing in the material before the fatigue tests. A modified linear elastic fracture-mechanics parameter, M, proposed by McEvily et al., was used to analyze the short FCG behavior under different stress ratios, R. The relation between the rate of FCG and M parameter was found to be useful and appropriate for predicting the fatigue lifetimes under different R ratios. Moreover, the probabilistic stress-fatigue life (P-S-N) curve of the material under different R ratios could be predicted with this method, which utilizes both the FCG law and a statistical distribution of sizes of the most dangerous intermetallic compounds. The evaluated results were in good agreement with the experimental ones. This correspondence indicates that the estimation method proposed in the present study is effective for evaluation of the probabilistic stress-fatigue life (P-S-N) curve of the material under different R ratios.
