Related papers: Tail Asymptotics and Estimation for Elliptical Dis…

Let (X_n,Y_n), n\ge 1 be bivariate random claim sizes with common distribution function F and let N(t), t \ge 0 be a stochastic process which counts the number of claims that occur in the time interval [0,t], t\ge 0. In this paper we derive…

We consider two different portfolios of proportional reinsurance of the same pool of risks. This contribution is concerned with Gaussian-like risks, which means that for large values the survival function of such risks is, up to a…

Models based on assumptions of multivariate regular variation and hidden regular variation provide ways to describe a broad range of extremal dependence structures when marginal distributions are heavy tailed. Multivariate regular variation…

Proliferating cell populations at steady state growth often exhibit broad protein distributions with exponential tails. The sources of this variation and its universality are of much theoretical interest. Here we address the problem by…

In survival or reliability studies, the mean residual life or life expectancy is an important characteristic of the model. Here, we study the limiting behaviour of the mean residual life, and derive an asymptotic expansion which can be used…

Let $P$ be a probability distribution on $\mathbb{R}^d$ (equipped with an Euclidean norm $|\cdot|$). Let $ r> 0 $ and let $(\alpha_n)_{n \geq1}$ be an (asymptotically) $L^r(P)$-optimal sequence of $n$-quantizers. We investigate the…

We find the exponential exact two-terms non-asymptotic expression for the maximum and minimum distribution of a non-Gaussian, in general case, random vector.

A random vector $X$ with representation $X=\sum_{j\geq0}A_jZ_j$ is considered. Here, $(Z_j)$ is a sequence of independent and identically distributed random vectors and $(A_j)$ is a sequence of random matrices, `predictable' with respect to…

The association between two random variables is often of primary interest in statistical research. In this paper semiparametric models for the association between random vectors X and Y are considered which leave the marginal distributions…

The exact expression for the probability density $p_{_N}(x)$ for sums of a finite number $N$ of random independent terms is obtained. It is shown that the very tail of $p_{_N}(x)$ has a Gaussian form if and only if all the random terms are…

The full moments expansion of the joint probability distribution of an isotropic random field, its gradient and invariants of the Hessian is presented in 2 and 3D. It allows for explicit expression for the Euler characteristic in ND and…

We compute the limiting distributions of the lengths of the longest monotone subsequences of random (signed) involutions with or without conditions on the number of fixed points (and negated points) as the sizes of the involutions tend to…

The article studies the almost surely asymptotics of extreme values $\bar{\xi}_n = \max_{1\leq i \leq n} \xi_i$, where $ \xi , \xi_1 , \xi_2 , \ldots$ are discrete identically distributed random variables. One of the main results on this…

We study clustering of the extremes in a stationary sequence with subexponential tails in the maximum domain of attraction of the Gumbel We obtain functional limit theorems in the space of random sup-measures and in the space $D(0,\infty)$.…

We characterize the second order subexponentiality of an infinitely divisible distribution on the real line under an exponential moment assumption. We investigate the asymptotic behaviour of the difference between the tails of an infinitely…

Let R be a positive random variable independent of S which is beta distributed. In this paper we are interested on the relation between the distribution function of R and that of RS. For this model we derive first some distributional…

We provide exact asymptotics for the tail probabilities $\mathbb{P} \{S_{n,r} > x\}$ as $x \to \infty$, for fix $n$, where $S_{n,r}$ is the $r$-trimmed partial sum of i.i.d. St. Petersburg random variables. In particular, we prove that…

We study the asymptotic behaviour of the maximum interpoint distance of random points in a planar bounded set with an unique major axis and a boundary behaving like an ellipse at the endpoints. Our main result covers the case of uniformly…

Let $Z_{n}$ be the number of individuals in a subcritical BPRE evolving in the environment generated by iid probability distributions. Let $X$ be the logarithm of the expected offspring size per individual given the environment. Assuming…

In this paper we introduce the class of W_p scale mixture random vectors with a particular radial decomposition and a independent splitting property specified by some random variable W_p, and a positive constant p. We derive several…