Related papers: Limit conditional distributions for bivariate vect…

A discrete version of the Gumbel (Type I) extreme value distribution has been derived by using the general approach of discretization of a continuous distribution. Important distributional and reliability properties have been explored. It…

Motivated by recent experiments with two-component Bose-Einstein condensates, we study fully-connected spin models subject to an additional constraint. The constraint is responsible for the Hilbert space dimension to scale only linearly…

For a bivariate random vector (X,Y), symmetry conditions are presented that yield stochastic orderings among |X|, |Y|, |max(X,Y)|, and | min(X, Y)|. Partial extensions of these results for multivariate random vectors (X1,...,Xn) are also…

The literature has covered the features and uses of the traditional univariate and bivariate logistic distributions in great detail. It is reasonable to wonder, though, if logistic marginals and conditionals could exhibit a similar…

We establish the limiting distribution (in total variation) of the quasi posteriors based on moment conditions, which only partially identify the parameters of interest. Some examples are discussed.

We study random normal matrix models whose eigenvalues tend to be distributed within a narrow "band" around the unit circle of width proportional to $\frac1n$, where $n$ is the size of matrices. For general radially symmetric potentials…

This article proposes a bivariate Simplex distribution for modeling continuous outcomes constrained to the interval $(0,1)$, which can represent proportions, rates, or indices. We derive analytical expressions to calculate the dependence…

In this paper, we considier the limiting distribution of the maximum interpoint Euclidean distance $M_n=\max _{1 \leq i<j \leq n}\left\|\boldsymbol{X}_i-\boldsymbol{X}_j\right\|$, where $\boldsymbol{X}_1, \boldsymbol{X}_2, \ldots,…

We consider the problem of determining the limiting spectral distribution for random matrices whose row distributions are permitted to have limited dependence. We assume mild moment conditions and give an extension of the…

Consider a random matrix $\mathbf{A}\in\mathbb{C}^{m\times n}$ ($m \geq n$) containing independent complex Gaussian entries with zero mean and unit variance, and let $0<\lambda_1\leq \lambda_{2}\leq ...\leq \lambda_n<\infty$ denote the…

We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…

Conditional Equi-concentration of Types on I-projections (ICET) and Extended Gibbs Conditioning Principle (EGCP) provide an extension of Conditioned Weak Law of Large Numbers and of Gibbs Conditioning Principle to the case of non-unique…

The asymptotic tail behaviour of sums of independent subexponential random variables is well understood, one of the main characteristics being the principle of the single big jump. We study the case of dependent subexponential random…

It will be recalled that the classical bivariate normal distributions have normal marginals and normal conditionals. It is natural to ask whether a similar phenomenon can be encountered involving Poisson marginals and conditionals.…

The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…

Simultaneous concurrence of extreme values across multiple climate variables can result in large societal and environmental impacts. Therefore, there is growing interest in understanding these concurrent extremes. In many applications, not…

We study the limit distribution of the largest fitness for two models of weakly correlated and identically distributed random fitnesses. The correlated fitness is given by a linear combination of a fixed number of independent random…

In this paper, we consider the empirical spectral distribution of the sample correlation matrix and investigate its asymptotic behavior under mild assumptions on the data's distribution, when dimension and sample size increase at the same…

The study of high-dimensional distributions is of interest in probability theory, statistics and asymptotic convex geometry, where the object of interest is the uniform distribution on a convex set in high dimensions. The $\ell^p$ spaces…

For nonstationary, strongly mixing sequences of random variables taking their values in a finite-dimensional Euclidean space, with the partial sums being normalized via matrix multiplication, with certain standard conditions being met, the…