Some asymptotic properties of the stable laws

1989 ◽  
pp. 229-238 ◽  
Author(s):  
A. V. Nagaev ◽  
S. M. Shkolnik
Keyword(s):  
Asymptotic Properties ◽  
Stable Laws

scholarly journals Pressure Function and Limit Theorems for Almost Anosov Flows

2021 ◽  
Vol 382 (1) ◽  
pp. 1-47
Author(s):  
Henk Bruin ◽  
Dalia Terhesiu ◽  
Mike Todd
Keyword(s):  
Thermodynamic Properties ◽  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Stable Laws ◽  
Analytic Framework ◽  
Pressure Function ◽  
Hyperbolic Flows ◽  
Anosov Flows ◽  
Almost Anosov

AbstractWe obtain limit theorems (Stable Laws and Central Limit Theorems, both standard and non-standard) and thermodynamic properties for a class of non-uniformly hyperbolic flows: almost Anosov flows, constructed here. The link between the pressure function and limit theorems is studied in an abstract functional analytic framework, which may be applicable to other classes of non-uniformly hyperbolic flows.

scholarly journals A Method for Confidence Intervals of High Quantiles

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 70
Author(s):  
Mei Ling Huang ◽  
Xiang Raney-Yan
Keyword(s):  
Confidence Intervals ◽  
Computational Algorithm ◽  
Geometric Mean ◽  
Asymptotic Properties ◽  
Quantile Estimation ◽  
Heavy Tailed Distributions ◽  
High Quantiles ◽  
High Quantile ◽  
Heavy Tailed ◽  
Infinite Moments

The high quantile estimation of heavy tailed distributions has many important applications. There are theoretical difficulties in studying heavy tailed distributions since they often have infinite moments. There are also bias issues with the existing methods of confidence intervals (CIs) of high quantiles. This paper proposes a new estimator for high quantiles based on the geometric mean. The new estimator has good asymptotic properties as well as it provides a computational algorithm for estimating confidence intervals of high quantiles. The new estimator avoids difficulties, improves efficiency and reduces bias. Comparisons of efficiencies and biases of the new estimator relative to existing estimators are studied. The theoretical are confirmed through Monte Carlo simulations. Finally, the applications on two real-world examples are provided.

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