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We consider the distribution of the major index on standard tableaux of arbitrary straight shape and certain skew shapes. We use cumulants to classify all possible limit laws for any sequence of such shapes in terms of a simple auxiliary…
The multivariate version of the Mixed Tempered Stable is proposed. It is a generalization of the Normal Variance Mean Mixtures. Characteristics of this new distribution and its capacity in fitting tails and capturing dependence structure…
Asymptotic distribution for the proportional covariance model under multivariate normal distributions is derived. To this end, the parametrization of the common covariance matrix by its Cholesky root is adopted. The derivations are made in…
Some problems relevant to the relativistic generalization of Maxwell's velocity distribution are discussed.
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.
Probability distributions supported on the simplex enjoy a wide range of applications across statistics and machine learning. Recently, a novel family of such distributions has been discovered: the continuous categorical. This family enjoys…
A distributional route to Gaussianity, associated with the concept of Conservative Mixing Transformations in ensembles of random vector-valued variables, is proposed. This route is completely different from the additive mechanism…
Consider a branching random walk in which the offspring distribution and the moving law both depend on an independent and identically distributed random environment indexed by the time.For the normalised counting measure of the number of…
Using a renormalization approach, we study the asymptotic limit distribution of the maximum value in a set of independent and identically distributed random variables raised to a power q(n) that varies monotonically with the sample size n.…
Reformulated uniform asymptotic expansions are derived for ordinary differential equations having a large parameter and a simple turning point. These involve Airy functions, but not their derivatives, unlike traditional asymptotic…
A new three parameter natural extension of the Conway-Maxwell-Poisson (COM-Poisson) distribution is proposed. This distribution includes the recently proposed COM-Poisson type negative binomial (COM-NB) distribution [Chakraborty, S. and…
The coupled Maxwell-Lorentz system describes feed-back action of electromagnetic fields in classical electrodynamics. When applied to point-charge sources (viewed as limiting cases of charged fluids) the resulting nonlinear weakly…
For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…
This paper extends Edgeworth-Cornish-Fisher expansions for the distribution and quantiles of nonparametric estimates in two ways. Firstly it allows observations to have different distributions. Secondly it allows the observations to be…
Different viewpoints on the asymptotic expansion of Feynman diagrams are reviewed. The relations between the field theoretic and diagrammatic approaches are sketched. The focus is on problems with large masses or large external momenta.…
The objective of this paper is the study of functions which only act on the digits of an expansion. In particular, we are interested in the asymptotic distribution of the values of these functions. The presented result is an extension and…
Maxwell's first derivation of the equilibrium distribution function for a dilute gas is generalized in the spirit of the nonextensive q-statistics proposed by Tsallis. As an application, the q-Doppler broadening of spectral lines due to the…
Local asymptotic minimax risk bounds in a locally asymptotically mixture of normal family of distributions have been investigated under asymmetric loss functions and the asymptotic distribution of the optimal estimator that attains the…
The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…
Here in this paper, it is tried to obtain and compare the ML estimations based on upper record values and a random sample. In continue, some theorems have been proven about the behavior of these estimations asymptotically.