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A Predictive Approach to Tail Probability Estimation
Extremes, 2001The problem of high quantiles estimation by an i.i.d. sample \(X_1\),\dots, \(X_n\) is considered. The authors propose a Bayesian approach where \(\Pr\{X-u \mid X>u\}\) is supposed to be a generalized Pareto distribution and the threshold \(u\) is a Bayesian parameter with some prior distribution.
de Zea Bermudes, P. +2 more
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Heavy Tails and Earthquake Probabilities
Seismological Research Letters, 2012The 21st century has already seen its share of devastating earthquakes, some of which have been labeled as “unexpected,” at least in the eyes of some seismologists and more than a few journalists. A list of seismological surprises could include the 2004 Sumatra-Andaman Islands; 2008 Wenchuan, China; 2009 Haiti; 2011 Christchurch, New Zealand; and 2011 ...
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Refinement of Convergence Rates for Tail Probabilities
Journal of Theoretical Probability, 2005There are many results aimed at providing necessary and sufficient conditions for the convergence of the sum \[ f(x)=\sum_n a_nP(|S_n|>xb_n),\;\;\;x>0, \] where \(S_n=X_1+\cdots+X_n,\) \(\{X,\;X_n;\;n\geq 1\}\) is a sequence of i.i.d. r.v., such that \(P(X\neq 0)>0,\;EX=0\;(E|X|0,\;\sum_n a_n=\infty\) and \(b_n\) is either \(n^{1/p},\;00,\) and so they
Li, Deli, Spătaru, Aurel
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Tail Probabilities for Regression Estimators [PDF]
Estimators of regression coefficients are known to be asymptotically normally distributed, provided certain regularity conditions are satisfied. In small samples and if the noise is not normally distributed, this can be a poor guide to the quality of the estimators.
Mikosch, Thomas Valentin +1 more
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Importance Sampling for Tail Probabilities
1991Abstract : Our interest is in the accurate and efficient evaluation of very small probabilities. Thus, we seek methods with bounded coefficient of variation as the probability decreases and we assess their performance. The univariate case is explored for a heuristic for construction of sampling density families.
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Probable predation on white-tailed kite by red-tailed hawk
1980(Uploaded by Plazi from the Biodiversity Heritage Library) No abstract provided.
Pinkston, D. Randall +1 more
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Saddlepoint Approximations to Density Functions, Tail Probabilities and Tail Expectations
2018In many applications in financial engineering, it is necessary to consider approximating the tail probabilities and tail expectations of random variables whose closed forms may not be tractable. Suppose the first few moments of the underlying distribution of a random variable are known, one may apply the Edgeworth type expansion up to the order of the ...
Yue Kuen Kwok, Wendong Zheng
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Tail probabilities of solutions to a generalized Ait-Sahalia interest rate model
, 2016N. Dung
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Second-order properties of tail probabilities of sums and randomly weighted sums
, 2015Tiantian Mao, K. Ng
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Markov's Inequality and Chebyshev's Inequality for Tail Probabilities: A Sharper Image
, 2015J. Cohen
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