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On Minimal-Moment Generating Functions
Springer Science and Business Media LLC - Tập 5 - Trang 145-155 - 2002
A formula expressing the inverse cumulative distribution function of a non-negative random variable in terms of contour integrals of its minimal-moment generating function is proved as well as an analog of the classical continuity theorem for characteristic functions.
Asymptotic Properties of Sums of Upper Records
Springer Science and Business Media LLC - Tập 6 - Trang 147-164 - 2003
Arnold and Villaseñor (1999) raised several questions for upper records, including characterizing all limit distributions of normalized partial sums of upper records. We provide some answers in the case when the distribution from which the samples are drawn is bounded above. When the distribution is not bounded above, we give sufficient conditions on the distribution for the properly normalized pa...... hiện toàn bộ
Light tails: all summands are large when the empirical mean is large
Springer Science and Business Media LLC - Tập 17 - Trang 305-336 - 2014
It is well known that for a fixed number of independent identically distributed summands with light tail, large values of the sample mean are obtained only when all the summands take large values. This paper explores this property as the number of summands tends to infinity. It provides the order of magnitude of the sample mean for which all summands are in some interval containing this value and ...... hiện toàn bộ
Functional limit theorems for the maxima of perturbed random walk and divergent perpetuities in the M 1-topology
Springer Science and Business Media LLC - Tập 20 - Trang 567-583 - 2017
Let (ξ
1, η
1), (ξ
2, η
2),… be a sequence of i.i.d. two-dimensional random vectors. In the earlier article Iksanov and Pilipenko (2014) weak convergence in the J
1-topology on the Skorokhod space of
...... hiện toàn bộ
Limit theorems for record counts and times in the F α -scheme
Springer Science and Business Media LLC - Tập 16 Số 2 - Trang 147-171 - 2013
Priority statement and some properties of t-lgHill estimator
Springer Science and Business Media LLC - Tập 23 - Trang 493-499 - 2020
We acknowledge the priority on the introduction of the formula of t-lgHill estimator for the positive extreme value index. We provide a novel motivation for this estimator based on ecologically driven dynamical systems. Another motivation is given directly by applying the general t-Hill procedure to log-gamma distribution. We illustrate the good quality of t-lgHill estimator in comparison to class...... hiện toàn bộ
Precise asymptotics for a type of order statistics
Springer Science and Business Media LLC - Tập 8 - Trang 327-338 - 2006
This paper obtains some results on the precise asymptotics for the order statistics generated by the random samples of maximum domain of attraction of the Fréchet distribution, which reveal the relations among the boundary function, weight function, convergence rate and limit position in a uniform form.
Max-stable processes and the functional D-norm revisited
Springer Science and Business Media LLC - Tập 18 - Trang 191-212 - 2014
Aulbach et al. (Extremes 16, 255283, 2013) introduced a max-domain of attraction approach for extreme value theory in C[0,1] based on functional distribution functions, which is more general than the approach based on weak convergence in de Haan and Lin (Ann. Probab. 29, 467483, 2001). We characterize this new approach by decomposing a process into its univariate margins and its copula process. In...... hiện toàn bộ
Location invariant Weiss-Hill estimator
Springer Science and Business Media LLC - Tập 15 Số 2 - Trang 197-230 - 2012
Asymptotic Expansions for the Distribution of the Maximum of Gaussian Random Fields
Springer Science and Business Media LLC - Tập 5 - Trang 181-212 - 2002
Some asymptotic results are proved for the distribution of the maximum of a centered Gaussian random field with unit variance on a compact subset S of ℝ
N
. They are obtained by a Rice method and the evaluation of some moments of the number of local maxima of the Gaussian field above an high level inside S and on the border ∂ S. Depending on the geometry of the bo...... hiện toàn bộ
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