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Approximating expected shortfall for heavy-tailed distributions
Econometrics and Statistics, 2018A saddlepoint approximation for evaluating the expected shortfall of financial returns under realistic distributional assumptions is derived. This addresses a need that has arisen after the Basel Committee’s proposed move from Value at Risk to expected shortfall as the mandated risk measure in its market risk framework.
Broda, Simon A +2 more
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Heavy-Tailed Distributions: Properties and Tests
Technometrics, 1974Distributions with heavier-than-exponential tails are studied for describing empirical phenomena. It is argued that the concept of increasing “conditional mean exceedance” provides a reasonable way of describing the heavy-tail phenomenon, and a family of Pareto distributions is shown to represent distributions for which this parameter is linearly ...
exaly +5 more sources
Communications in statistics. Simulation and computation, 2020
Heavy tailed distributions play very significant role in the study of actuarial and financial risk management data but the probability distributions proposed to model such data are scanty. Actuaries often search for new and appropriate statistical models
Zubair Ahmad, E. Mahmoudi, S. Dey
semanticscholar +1 more source
Heavy tailed distributions play very significant role in the study of actuarial and financial risk management data but the probability distributions proposed to model such data are scanty. Actuaries often search for new and appropriate statistical models
Zubair Ahmad, E. Mahmoudi, S. Dey
semanticscholar +1 more source
Mean Estimation and Regression Under Heavy-Tailed Distributions: A Survey
Foundations of Computational Mathematics, 2019We survey some of the recent advances in mean estimation and regression function estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data in both the univariate and multivariate settings.
G. Lugosi, S. Mendelson
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Inverse Laplace transform for heavy-tailed distributions
Applied Mathematics and Computation, 2004Here the Laplace transform inversion on the real line of heavy-tailed (probability) density functions is considered. The method assumes as known a finite set of fractional moments drawn from real values of the Laplace transform by fractional calculus.
Tagliani, Aldo, Y. VELAZQUEZ
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2021
In Sec. 2.3.3 we introduced the idea of heavy-tailed distributions from a purely mathematical point of view, where we considered probability distributions for which the central limit theorem does not apply. The terminology arises because the “tails” of the distribution, that is the parts where the variable |x| → ∞, decrease so slowly that in most cases
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In Sec. 2.3.3 we introduced the idea of heavy-tailed distributions from a purely mathematical point of view, where we considered probability distributions for which the central limit theorem does not apply. The terminology arises because the “tails” of the distribution, that is the parts where the variable |x| → ∞, decrease so slowly that in most cases
openaire +1 more source
Inference for heavy tailed distributions
Journal of Statistical Planning and Inference, 1998This work develops the statistical inference for stable laws of order \(\alpha\) and an asymmetry parameter \(\beta\), based on an independent sample of size \(n\geq 1\). Three different approaches to the construction of confidence intervals for the mean \(\mu\) are proposed, two of them involving bootstrap.
Athreya, K. B., Lahiri, S. N., Wu, Wei
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Risk aggregation and stochastic dominance for a class of heavy-tailed distributions
ASTIN Bulletin: The Journal of the International Actuarial AssociationWe introduce a new class of heavy-tailed distributions for which any weighted average of independent and identically distributed random variables is larger than one such random variable in (usual) stochastic order.
Yuyu Chen, S. Shneer
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