Related papers: Expansions of maximum and minimum from Generalized…
The skew-normal and related families are flexible and asymmetric parametric models suitable for modelling a diverse range of systems. We show that the multivariate maximum of a high-dimensional extended skew-normal random sample has…
In this manuscript, we study the limiting distribution for the joint law of the largest and the smallest singular values for random circulant matrices with generating sequence given by independent and identically distributed random elements…
Two relativistic distributions which generalizes the Maxwell Boltzman (MB) distribution are analyzed: the relativistic MB and the Maxwell-J{\"u}ttner (MJ) distribution. For the two distributions we derived in terms of special functions the…
This paper investigates the asymptotic behavior of the extremes of a sequence of generalized Oppenheim random variables. Particularly, we establish conditions under which some normalized extremes of sequences arising from Oppenheim…
In several variables, we prove the pointwise convergence of multiresolution expansions to the distributional point values of tempered distributions and distributions of superexponential growth. The article extends and improves earlier…
If the Euclidean norm is strongly concentrated with respect to a measure, the average distribution of an average marginal of this measure has Gaussian asymptotics that captures tail behaviour. If the marginals of the measure have…
This paper introduces an extension to the normal distribution through the polar method to capture bimodality and asymmetry, which are often observed characteristics of empirical data. The later two features are entirely controlled by a…
Generalized likelihoods are commonly used to obtain consistent estimators with attractive computational and robustness properties. Formally, any generalized likelihood can be used to define a generalized posterior distribution, but an…
In this paper, we investigated the effect on extreme of random replacing for a stationary sequence satisfying a type of long dependent condition and a local dependent condition, and derived the joint asymptotic distribution of maximum from…
In this paper, we consider the distribution of the supremum of non-stationary Gaussian processes, and present a new theoretical result on the asymptotic behaviour of this distribution. Unlike previously known facts in this field, our main…
We obtain an asymptotic normality result that reveals the precise asymptotic behavior of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects. In achieving the…
We define a type of generalized asymptotic series called $v$-asymptotic. We show that every function with moderate growth at infinity has a $v$-asymptotic expansion. We also describe the set of $v$-asymptotic series, where a given function…
We consider the steady states of a driven inelastic Maxwell gas consisting of two types of particles with scalar velocities. Motivated by experiments on bilayers where only one layer is driven, we focus on the case when only one of the two…
For positive integers $d$ and $p$ such that $d \ge p$, let $\mathbb{R}^{d \times p}$ denote the set of $d \times p$ real matrices, $I_p$ be the identity matrix of order $p$, and $V_{d,p} = \{x \in \mathbb{R}^{d \times p} \mid x'x = I_p\}$…
The paper presents a novel asymptotic distribution for a mle when the log--likelihood is strictly concave in the parameter for all data points; for example, the exponential family. The new asymptotic distribution can be seen as a refinement…
In this paper, joint asymptotics of powered maxima for a triangular array of bivariate powered Gaussian random vectors are considered. Under the H\"usler-Reiss condition, limiting distributions of powered maxima are derived. Furthermore,…
We determine the asymptotic distribution of the sum of correlated variables described by a matrix product ansatz with finite matrices, considering variables with finite variances. In cases when the correlation length is finite, the law of…
This paper establishes a strict mathematical relationship between an arbitrary continuous function on a compact set and its global minima, like the well-known first order optimality condition for convex and differentiable functions. By…
Multivariate generalized Pareto distributions arise as the limit distributions of exceedances over multivariate thresholds of random vectors in the domain of attraction of a max-stable distribution. These distributions can be parametrized…
A well-known result across information theory, machine learning, and statistical physics shows that the maximum entropy distribution under a mean constraint has an exponential form called the Gibbs-Boltzmann distribution. This is used for…