scholarly journals Asymptotic properties of rapidly varying functions

2013 ◽  
Vol 17 (2) ◽  
pp. 75-78
Author(s):  
Vladimir Vladicic ◽  
Nebojsa Elez
Keyword(s):  
Asymptotic Properties ◽  
Rapidly Varying Functions

scholarly journals Integral properties of rapidly and regularly varying functions

2015 ◽  
Vol 98 (112) ◽  
pp. 91-96 ◽  
Author(s):  
Nebojsa Elez ◽  
Vladimir Vladicic
Keyword(s):  
Asymptotic Properties ◽  
Regularly Varying Functions ◽  
Regularly Varying ◽  
Rapidly Varying Functions

Regularly and rapidly varying functions are studied as well as the asymptotic properties related to, several classical inequalities and integral sums.

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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