On conditional extreme values of random vectors with polar representation

Extremes ◽  
2013 ◽  
Vol 17 (2) ◽  
pp. 193-219 ◽  
Author(s):  
Miriam Isabel Seifert
Keyword(s):  
Extreme Values ◽  
Random Vectors ◽  
Polar Representation

scholarly journals Large deviations of bivariate Gaussian extrema

2019 ◽  
Vol 93 (3-4) ◽  
pp. 333-349 ◽  
Author(s):  
Remco van der Hofstad ◽  
Harsha Honnappa
Keyword(s):  
Large Deviations ◽  
Simulation Analysis ◽  
Extreme Values ◽  
Rate Function ◽  
Tail Asymptotics ◽  
Random Vectors ◽  
Large Deviations Principle ◽  
Tail Event ◽  
Infinite Server Queues ◽  
Steady State Performance

Abstract We establish sharp tail asymptotics for componentwise extreme values of bivariate Gaussian random vectors with arbitrary correlation between the components. We consider two scaling regimes for the tail event in which we demonstrate the existence of a restricted large deviations principle and identify the unique rate function associated with these asymptotics. Our results identify when the maxima of both coordinates are typically attained by two different versus the same index, and how this depends on the correlation between the coordinates of the bivariate Gaussian random vectors. Our results complement a growing body of work on the extremes of Gaussian processes. The results are also relevant for steady-state performance and simulation analysis of networks of infinite server queues.

Equation of state of a nonideal plasma for extreme values of the parameters

1985 ◽  
Vol 147 (9) ◽  
pp. 192
Author(s):  
Vladimir E. Fortov
Keyword(s):  
Equation Of State ◽  
Extreme Values ◽  
Nonideal Plasma

EXTREME VALUES OF SEA SURFACE TEMPERATURE ASSOCIATED WITH LONG-PERIOD PHENOMENA OCCURRED DURING 1960-2015 IN THE COLOMBIAN PACIFIC OCEAN

2017 ◽  
Author(s):  
Diaz Juan Navia ◽  
Diaz Juan Navia ◽  
Bolaños Nancy Villegas ◽  
Bolaños Nancy Villegas ◽  
Igor Malikov ◽  
...  
Keyword(s):  
Time Series ◽  
Pacific Ocean ◽  
Surface Temperature ◽  
Sea Surface Temperature ◽  
Extreme Values ◽  
Sea Surface ◽  
Absolute Maximum ◽  
Data Set ◽  
Arctic Oscillation Index ◽  
Colombian Pacific

Sea Surface Temperature Anomalies (SSTA), in four coastal hydrographic stations of Colombian Pacific Ocean, were analyzed. The selected hydrographic stations were: Tumaco (1°48'N-78°45'W), Gorgona island (2°58'N-78°11'W), Solano Bay (6°13'N-77°24'W) and Malpelo island (4°0'N-81°36'W). SSTA time series for 1960-2015 were calculated from monthly Sea Surface Temperature obtained from International Comprehensive Ocean Atmosphere Data Set (ICOADS). SSTA time series, Oceanic Nino Index (ONI), Pacific Decadal Oscillation index (PDO), Arctic Oscillation index (AO) and sunspots number (associated to solar activity), were compared. It was found that the SSTA absolute minimum has occurred in Tumaco (-3.93°C) in March 2009, in Gorgona (-3.71°C) in October 2007, in Solano Bay (-4.23°C) in April 2014 and Malpelo (-4.21°C) in December 2005. The SSTA absolute maximum was observed in Tumaco (3.45°C) in January 2002, in Gorgona (5.01°C) in July 1978, in Solano Bay (5.27°C) in March 1998 and Malpelo (3.64°C) in July 2015. A high correlation between SST and ONI in large part of study period, followed by a good correlation with PDO, was identified. The AO and SSTA have showed an inverse relationship in some periods. Solar Cycle has showed to be a modulator of behavior of SSTA in the selected stations. It was determined that extreme values of SST are related to the analyzed large scale oscillations.

Optimal Model-Free Approach Based on MDL and CHL for Active Brain Identification in fMRI Data Analysis

2020 ◽  
Vol 16 ◽  
Author(s):  
Hussain A. Jaber ◽  
Ilyas Çankaya ◽  
Hadeel K. Aljobouri ◽  
Orhan M. Koçak ◽  
Oktay Algin
Keyword(s):  
Data Analysis ◽  
Time Course ◽  
Extreme Values ◽  
Statistical Parametric Mapping ◽  
Fmri Data ◽  
Cluster Center ◽  
Jaccard Coefficient ◽  
Neural Gas ◽  
Model Free ◽  
Clustering Approach

Background: Cluster analysis is a robust tool for exploring the underlining structures in data and grouping them with similar objects. In the researches of Functional Magnetic Resonance Imaging (fMRI), clustering approaches attempt to classify voxels depending on their time-course signals into a similar hemodynamic response over time. Objective: In this work, a novel unsupervised learning approach is proposed that relies on using Enhanced Neural Gas (ENG) algorithm in fMRI data for comparison with Neural Gas (NG) method, which has yet to be utilized for that aim. The ENG algorithm depends on the network structure of the NG and concentrates on an efficacious prototype-based clustering approach. Methods: The comparison outcomes on real auditory fMRI data show that ENG outperforms the NG and statistical parametric mapping (SPM) methods due to its insensitivity to the ordering of input data sequence, various initializations for selecting a set of neurons, and the existence of extreme values (outliers). The findings also prove its capability to discover the exact and real values of a cluster number effectively. Results: Four validation indices are applied to evaluate the performance of the proposed ENG method with fMRI and compare it with a clustering approach (NG algorithm) and model-based data analysis (SPM). These validation indices include the Jaccard Coefficient (JC), Receiver Operating Characteristic (ROC), Minimum Description Length (MDL) value, and Minimum Square Error (MSE). Conclusion: The ENG technique can tackle all shortcomings of NG application with fMRI data, identify the active area of the human brain effectively, and determine the locations of the cluster center based on the MDL value during the process of network learning.

Hydrogen peroxide decomposition on a two-component CuO-Cr2O3 catalyst

1988 ◽  
Vol 53 (8) ◽  
pp. 1636-1646 ◽  
Author(s):  
Viliam Múčka ◽  
Kamil Lang
Keyword(s):  
Hydrogen Peroxide ◽  
Catalytic Activity ◽  
Extreme Values ◽  
Catalytic Properties ◽  
Active Components ◽  
Catalytic Systems ◽  
Heterogeneous Catalytic ◽  
Peroxide Decomposition ◽  
Two Component ◽  
Catalytically Active

Some physical and catalytic properties of the two-component copper(II)oxide-chromium(III)oxide catalyst with different content of both components were studied using the decomposition of the aqueous solution of hydrogen peroxide as a testing reaction. It has been found that along to both basic components, the system under study contains also the spinel structure CuCr2O4, chromate washable by water and hexavalent ions of chromium unwashable by water. The soluble chromate is catalytically active. During the first period of the reaction the equilibrium is being established in both homogeneous and heterogeneous catalytic systems. The catalytic activity as well as the specific surface area of the washed solid is a non-monotonous function of its composition. It seems highly probable that the extreme values of both these quantities are not connected with the detected admixtures in the catalytic system. The system under study is very insensitive with regard to the applied doses of gamma radiation. Its catalytic properties are changed rather significantly after the thermal treatment and particularly after the partial reduction to low degree by hydrogen. The observed changes of the catalytic activity of the system under study are very probably in connection with the changes of the valence state of the catalytically active components of the catalyst.

A new unbiased additive robust volatility estimation using extreme values of asset prices

2020 ◽  
Vol 34 (3) ◽  
pp. 313-347
Author(s):  
Muneer Shaik ◽  
S. Maheswaran
Keyword(s):  
Asset Prices ◽  
Extreme Values ◽  
Volatility Estimation

POWER LAW AND STRETCHED EXPONENTIAL EFFECTS OF EXTREME EVENTS IN CHINESE STOCK MARKETS

2010 ◽  
Vol 09 (02) ◽  
pp. 203-217 ◽  
Author(s):  
XIAOJUN ZHAO ◽  
PENGJIAN SHANG ◽  
YULEI PANG
Keyword(s):  
Correlation Analysis ◽  
Power Law ◽  
Extreme Events ◽  
Stock Markets ◽  
Cross Correlation ◽  
Extreme Values ◽  
Cumulative Distribution ◽  
Stretched Exponential ◽  
Cross Correlation Analysis ◽  
Chinese Stock Markets

This paper reports the statistics of extreme values and positions of extreme events in Chinese stock markets. An extreme event is defined as the event exceeding a certain threshold of normalized logarithmic return. Extreme values follow a piecewise function or a power law distribution determined by the threshold due to a crossover. Extreme positions are studied by return intervals of extreme events, and it is found that return intervals yield a stretched exponential function. According to correlation analysis, extreme values and return intervals are weakly correlated and the correlation decreases with increasing threshold. No long-term cross-correlation exists by using the detrended cross-correlation analysis (DCCA) method. We successfully introduce a modification specific to the correlation and derive the joint cumulative distribution of extreme values and return intervals at 95% confidence level.

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