Related papers: Exact Tail Asymptotics of Dirichlet Distributions

Let (RU_1, R U_2) be a given bivariate scale mixture random vector, with R>0 being independent of the bivariate random vector (U_1,U_2). In this paper we derive exact asymptotic expansions of the tail probability P{RU_1> x, RU_2> ax}, a \in…

In this paper we consider elliptical random vectors X in R^d,d>1 with stochastic representation A R U where R is a positive random radius independent of the random vector U which is uniformly distributed on the unit sphere of R^d and A is a…

The class of Dirichlet random vectors is central in numerous probabilistic and statistical applications. The main result of this paper derives the exact tail asymptotics of the aggregated risk of powers of Dirichlet random vectors when the…

Let (X,Y) be a bivariate elliptical random vector with associated random radius in the Gumbel max-domain of attraction. In this paper we obtain a second order asymptotic expansion of the joint survival probability P(X > x, Y> y) for x,y…

Let $\eta_1$, $\eta_2,\ldots$ be independent copies of a random variable $\eta$ with zero mean and finite variance which is bounded from the right, that is, $\eta\leq b$ almost surely for some $b>0$. Considering different types of the…

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…

Let $\{X(t)= (X_1(t),X_2(t))^T,\ t \in \mathbb{R}^N\}$ be an $\mathbb{R}^2$-valued continuous locally stationary Gaussian random field with $\mathbb{E}[X(t)]=\mathbf{0}$. For any compact sets $A_1, A_2 \subset \mathbb{R}^N$, precise…

We provide asymptotic theory for the joint distribution of $X_{\mathrm{inv}}$ and $X_{\mathrm{des}}$, the numbers of inversions and descents of random permutations. Recently, D\"orr & Kahle (2022) proved that $X_{\mathrm{inv}}$,…

An infinite convergent sum of independent and identically distributed random variables discounted by a multiplicative random walk is called perpetuity, because of a possible actuarial application. We give three disjoint groups of sufficient…

We obtain in this paper using the saddle point method the expression for the exact asymptotic for the tail of maximum of smooth (twice continuous differentiable) random field (process) distribution.

We derive the asymptotic expansion at infinity for embedded ends of uniformly elliptic Weingarten surfaces with finite total curvature in $\mathbb{R}^3$, and we establish a maximum principle at infinity. Furthermore, we solve the Dirichlet…

We consider a one-dimensional random walk $S_n$ with i.i.d. increments with zero mean and finite variance. We study the asymptotic expansion for the tail distribution $\mathbf P(\tau_x>n)$ of the first passage times…

A simple estimator for the finite right endpoint of a distribution function in the Gumbel max-domain of attraction is proposed. Large sample properties such as consistency and the asymptotic distribution are derived. A simulation study is…

We study the asymptotic behavior of the diameter or maximum interpoint distance of a cloud of i.i.d. $d$-dimensional random vectors when the number of points in the cloud tends to infinity. This is a non standard extreme value problem since…

In this paper we generalize the result of directional transience from [SabotTournier10]. This enables us, by means of [Simenhaus07], [ZernerMerkl01] and [Bouchet12] to conclude that, on Z^d (for any dimension d), random walks in i.i.d.…

We consider the sums $S_n=\xi_1+\cdots+\xi_n$ of independent identically distributed random variables. We do not assume that the $\xi$'s have a finite mean. Under subexponential type conditions on distribution of the summands, we find the…

We study the tail behavior of the distribution of the sum of asymptotically independent risks whose marginal distributions belong to the maximal domain of attraction of the Gumbel distribution. We impose conditions on the distribution of…

Let F be a distribution function with negative mean and regularly varying right tail. Under a mild smoothness condition we derive higher order asymptotic expansions for the tail distribution of the maxima of the random walk generated by F.…

By using a probabilistic technique based on the exponential change of measure we find a precise tail asymptotic behavior of some perpetuities with distributions close to the Dickman distribution.

We establish some asymptotic expansions for infinite weighted convolution of distributions having regular varying tails. Various applications to statistics and probability are developed.