Related papers: Distributions of statistics on separable permutati…
Consider a set of order statistics that arise from sorting samples from two different populations, each with their own, possibly different distribution function. The probability that these order statistics fall in disjoint, ordered…
Generalized Maxwell distribution is an extension of the classic Maxwell distribution. In this paper, we concentrate on the joint distributional asymptotics of normalized maxima and minima. Under optimal normalizing constants, asymptotic…
One of the most central result in combinatorics says that the descent statistic and the excedance statistic are equidistribued over the symmetric group. As a continuation of the work of Shareshian-Wachs (Adv. Math., 225(6) (2010),…
In this note, we prove some and conjecture other results regarding the distribution of descent top and descent bottom sets on some pattern-avoiding permutations. In particular, for 3-letter patterns, we show bijectively that the set of…
Two closely related discrete probability distributions are introduced. In each case the support is a set of vectors in $\mathbb{R}^n$ obtained from the partitions of the fixed positive integer $n$. These distributions arise naturally when…
The distribution of descents in a fixed conjugacy class of $S_n$ is studied, and it is shown that its moments have an interesting property. A particular conjugacy class that is of interest is the class of matchings (also known as fixed…
We consider a multinomial distribution, where the number of cells increases and the cell-probabilities decreases as the number of observations grows. The probabilities of large deviations of statistics, which has form of a sum of Borel…
Two semimetrics on probability distributions are proposed, given as the sum of differences of expectations of analytic functions evaluated at spatial or frequency locations (i.e, features). The features are chosen so as to maximize the…
In [S. Kitaev and J. Remmel: Classifying descents according to parity] the authors refine the well-known permutation statistic "descent" by fixing parity of (exactly) one of the descent's numbers. In this paper, we generalize the results of…
Permutations of correlated sequences of random variables appear naturally in a variety of applications such as graph matching and asynchronous communications. In this paper, the asymptotic statistical behavior of such permuted sequences is…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
Every observation may follow a distribution that is randomly selected in a class of distributions. It is called the distribution uncertainty. This is a fact acknowledged in some research fields such as financial risk measure. Thus, the…
A simple and transparent derivation of the formally exact probability distribution for classical non-equilibrium systems is given. The corresponding stochastic, dissipative equations of motion are also derived.
We study the joint distribution of descents and inverse descents over the set of permutations of n letters. Gessel conjectured that the two-variable generating function of this distribution can be expanded in a given basis with nonnegative…
We define new statistics, (c, d)-descents, on the colored permutation groups Z_r \wr S_n and compute the distribution of these statistics on the elements in these groups. We use some combinatorial approaches, recurrences, and generating…
Four new probability models are derived which generalize the common univariate continuous distributions. Classical distributional measures are derived from Hoel, et al., Introduction to Probability Theory, 1971. Measures include probability…
We discuss the classical statistics of isolated subsystems. Only a small part of the information contained in the classical probability distribution for the subsystem and its environment is available for the description of the isolated…
The probability distributions of the masses of the clusters spanning from top to bottom of a percolating lattice at the percolation threshold are obtained in all dimensions from two to five. The first two cumulants and the exponents for the…
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…
We investigate the statistics of trees grown from some initial tree by attaching links to preexisting vertices, with attachment probabilities depending only on the valence of these vertices. We consider the asymptotic mass distribution that…