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Weak properties and robustness of t-Hill estimators
Springer Science and Business Media LLC - - 2016
We describe a novel method of heavy tails estimation based on transformed score (t-score). Based on a new score moment method we derive the t-Hill estimator, which estimates the extreme value index of a distribution function with regularly varying tail. t-Hill estimator is distribution sensitive, thus it differs in e.g. Pareto and log-gamma case. Here, we study both forms of the estimator, i.e. t-......
Exact asymptotics of component-wise extrema of two-dimensional Brownian motion
Springer Science and Business Media LLC - Tập 23 - Trang 569-602 - 2020
We derive the exact asymptotics of
$ {\mathbb {P} \left \{ \underset {t\ge 0}{\sup } \left (X_{1}(t) - \mu _{1} t\right )> u, \ \underset {s\ge 0}{\sup } \left (X_{2}(s) - \mu _{2} s\right )> u \right \} },\ \ u\to \infty , $
where (X1(t), X2(s))t, s≥ 0 is a correlated two-dimensional Brownian motion with correlation ρ ∈ [− 1,1] and μ1, μ2 > 0. It appears that the play between ρ and μ1, μ2 lead......
Comments to Rootzén & Zholud: Human life is unlimited – but short
Springer Science and Business Media LLC - Tập 21 - Trang 383-386 - 2018
On the regular variation of ratios of jointly Fréchet random variables
Springer Science and Business Media LLC - - 2012
Tail asymptotics for the sum of two heavy-tailed dependent risks
Springer Science and Business Media LLC - Tập 9 - Trang 107-130 - 2006
Let X
1
, X
2 denote positive heavy-tailed random variables with continuous marginal distribution functions F
1 and F
2, respectively. The asymptotic behavior of the tail of X
1
+X
2 is studied in a general copula framework and some bounds and extremal properties are prov......
Distribution of the height of local maxima of Gaussian random fields
Springer Science and Business Media LLC - Tập 18 - Trang 213-240 - 2014
Let {f(t) : t ∈ T} be a smooth Gaussian random field over a parameter space T, where T may be a subset of Euclidean space or, more generally, a Riemannian manifold. We provide a general formula for the distribution of the height of a local maximum ℙ{f(t
0) > u|t
0 is a local maximum of f(t)} when f is non-stationary. Moreover, we establish asymptotic approximations ......
Asymptotics of convolution with the semi-regular-variation tail and its application to risk
Springer Science and Business Media LLC - Tập 21 - Trang 509-532 - 2018
In this paper, according to a certain criterion, we divide the exponential distribution class into some subclasses. One of them is closely related to the regular-variation-tailed distribution class, and is called the semi-regular-variation-tailed distribution class. The new class possesses several nice properties, although distributions in it are not convolution equivalent. We give the precise tai......
Large Deviation Probabilities for Square-Gaussian Stochastic Processes
Springer Science and Business Media LLC - - 1999
We investigate properties of square-Gaussian stochastic processes. These processes are formed by quadratic forms of Gaussian processes or by limits in the mean square of quadratic forms of Gaussian processes. Special classes of these processes are determined and investigated. For processes from these classes estimates of large deviation probability are obtained. These estimates we use to estimate ......
Polynomial power-Pareto quantile function models
Springer Science and Business Media LLC - Tập 13 - Trang 291-314 - 2009
In this paper we propose a polynomial power-Pareto quantile function model and a Bayesian method for parameters estimation. We also carried out simulation studies and applied our methodology to real data sets empirically. The results show that a quantile function approach to statistical modelling is very flexible due to the properties of quantile functions, and that the combination of a power and ......
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