Self-similar processes in collective risk theory.
Shape factor extremes for prolate spheroids
Microscopic prolate spheroids in a given volume of an opaque material are considered. The extremes of the shape factor of the spheroids are studied. The profiles of the spheroids are observed on a random planar section and based on these observations we want to estimate the distribution of the extremal shape factor of the spheroids. We show that under a tail uniformity condition the Maximum domain of attraction is stable. We discuss the normalising constants (n.c.) for the extremes of the spheroid...
Some results on the influence of extremes on the bootstrap
Stability and contagion measures for spatial extreme value analyzes
As part of global climate change an accelerated hydrologic cycle (including an increase in heavy precipitation) is anticipated (Trenberth [20, 21]). So, it is of great importance to be able to quantify high-impact hydrologic relationships, for example, the impact that an extreme precipitation (or temperature) in a location has on a surrounding region. Building on the Multivariate Extreme Value Theory we propose a contagion index and a stability index. The contagion index makes it possible to quantify...
Stein estimation for infinitely divisible laws
Unbiased risk estimation, à la Stein, is studied for infinitely divisible laws with finite second moment.
Stereology of extremes; size of spheroids
The prediction of size extremes in Wicksell’s corpuscle problem with oblate spheroids is considered. Three-dimensional particles are represented by their planar sections (profiles) and the problem is to predict their extremal size under the assumption of a constant shape factor. The stability of the domain of attraction of the size extremes is proved under the tail equivalence condition. A simple procedure is proposed of evaluating the normalizing constants from the tail behaviour of appropriate...
Stochastic ordering of random kth record values
Let be a sequence of independent and identically distributed random variables with continuous distribution function F(x). Denote by X(1,k),X(2,k),... the kth record values corresponding to We obtain some stochastic comparison results involving the random kth record values X(N,k), where N is a positive integer-valued random variable which is independent of the .
Sums of extreme values of subordinated long-range dependent sequences: moving averages with finite variance.
Sur les vitesses de convergence en théorie des valeurs extrêmes.
Survival probability approach to the relaxation of a macroscopic system in the defect-diffusion framework
The main objective of this paper is to present a new probabilistic model underlying the universal relaxation laws observed in many fields of science where we associate the survival probability of the system's state with the defect-diffusion framework. Our approach is based on the notion of the continuous-time random walk. To derive the properties of the survival probability of a system we explore the limit theorems concerning either the summation or the extremes: maxima and minima. The forms of...