Related papers: Limit conditional distributions for bivariate vect…
We study analytically and numerically the extreme value distribution of observables defined along the temporal evolution of a dynamical system. The convergence to the Gumbel law of observable recurrences gives information on the fractal…
The problem of estimating the exponent of a stable law received a considerable attention in the recent literature. Here, we deal with an estimate of such a exponent introduced by De Haan and Resnick when the corresponding distribution…
Although the specification of bivariate probability models using a collection of assumed conditional distributions is not a novel concept, it has received considerable attention in the last decade. In this study, a bivariate…
The multidimensional distributions with heavy tails attracted recently the attention of several papers on Applied Probability. However, the most of the works of the last decades are focused on multivariate regular variation, while the rest…
The classical multivariate extreme value theory tries to capture the extremal dependence between the components under a multivariate domain of attraction condition and it requires each of the components to be in the domain of attraction of…
In this note, we establish the convergence in distribution of the maxima of i.i.d. random variables to the Gumbel distribution with the associated normalizing sequences for several examples that are related to the normal distribution.…
We consider component-wise equivariant estimation of order restricted location/scale parameters of a general bivariate distribution under quite general conditions on underlying distributions and the loss function. This paper unifies various…
We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric problems are discussed.
In this work, we derive some novel properties of the bimodal normal distribution. Some of its mathematical properties are examined. We provide a formal proof for the bimodality and assess identifiability. We then discuss the maximum…
The proposed paper discusses the problem of discrimination between close hypotheses about distributions belonging to the Gumbel maximum domain of attraction. The distinctive feature of the proposed work is using only k higher order…
In extreme values theory, for a sufficiently large block size, the maxima distribution is approximated by the generalized extreme value (GEV) distribution. The GEV distribution is a family of continuous probability distributions, which has…
We consider sequences of random variables whose probability generating functions are polynomials all of whose roots lie on the unit circle. The distribution of such random variables has only been sporadically studied in the literature. We…
A pedagogical account of some aspects of Extreme Value Statistics (EVS) is presented from the somewhat non-standard viewpoint of Large Deviation Theory. We address the following problem: given a set of $N$ i.i.d. random variables…
We study vectors chosen at random from a compact convex polytope in $\mathbb{R}^n$ given by a finite number of linear constraints. We determine which projections of these random vectors are asymptotically normal as $n\to\infty$. Marginal…
Consider the set of Borel probability measures on $\mathbf{R}^k$ and endow it with the topology of weak convergence. We show that the subset of all probability measures which belong to the domain of attraction of some multivariate extreme…
We study the limiting behavior of a Bienayme-Galton-Watson tree conditioned to have a large number of vertices and either a fixed number of leaves or a fixed number of internal nodes. The first biconditioning gives a universal result with…
\noindent We study the asymptotic behavior of a sum of independent and identically distributed random variables conditioned by a sum of independent and identically distributed integer-valued random variables. We prove a Berry-Esseen bound…
Models for extreme values are generally derived from limit results, which are meant to be good enough approximations when applied to finite samples. Depending on the speed of convergence of the process underlying the data, these…
Consider two random variables following Skellam distributions of parameters going to infinity linearly. We prove that the limit distribution of the first variable, conditionally on being equal to the second, is Gaussian.
An equivalent condition for the product of elements of an independent random sample on a compact algebraic group converging in distribution to some random variable as the sample size increases is obtained. Namely, a limit distribution…