Related papers: New Probabilistic Inequalities from Monotone Likel…
In this paper, I present a completely new type of upper and lower bounds on the right-tail probabilities of continuous random variables with unbounded support and with semi-bounded support from the left. The presented upper and lower…
Let $A_n= \varepsilon_n \cdots \varepsilon_1$, where $(\varepsilon_n)_{n \geq 1}$ is a sequence of independent random matrices taking values in $ GL_d(\mathbb R)$, $d \geq 2$, with common distribution $\mu$. In this paper, under standard…
Moment inequalities play important roles in probability limit theory and mathematical statistics. In this work, the von Bahr-Esseen type inequality for extended negatively dependent random variables under sub-linear expectations is…
Several probability distributions have been proposed in the literature, especially with the aim of obtaining models that are more flexible relative to the behaviors of the density and hazard rate functions. Recently, a new generalization of…
We present a new proof of the Burkholder-Davis-Gundy inequalities for $1\leq p<\infty$. The novelty of our method is that these martingale inequalities are obtained as consequences of elementary deterministic counterparts. The latter have a…
We derive the most probable distribution of resources for a simple society. We find that a probabilistic analysis forbids both too much and too less equity, and selects instead a minimally ordered state. We give the detailed calculations…
This article is a survey of results concerning an inequality, which may be seen as a versatile tool to solve problems in the domain of Applied Probability. The inequality, which we call BRS-inequality, gives a convenient upper bound for the…
This paper develops a general methodology to conduct statistical inference for observations indexed by multiple sets of entities. We propose a novel multiway empirical likelihood statistic that converges to a chi-square distribution under…
The main purpose of this paper is to propose a variance-based Bregman extragradient algorithm with line search for solving stochastic variational inequalities, which is robust with respect an unknown Lipschitz constant. We prove the almost…
In this paper we show that the weighted Bernstein-Walsh inequality in logarithmic potential theory is sharp up to some new universal constant, provided that the external field is given by a logarithmic potential. Our main tool for such…
We present a new concentration of measure inequality for sums of independent bounded random variables, which we name a split-kl inequality. The inequality is particularly well-suited for ternary random variables, which naturally show up in…
In the standard Bayesian framework data are assumed to be generated by a distribution parametrized by $\theta$ in a parameter space $\Theta$, over which a prior distribution $\pi$ is given. A Bayesian statistician quantifies the belief that…
Total probability and Bayes formula are two basic tools for using prior information in the Bayesian statistics. In this paper we introduce an alternative tool for using prior information. This new toold enables us to improve some…
Given a random quantum state of multiple distinguishable or indistinguishable particles, we provide an effective method, rooted in symplectic geometry, to compute the joint probability distribution of the eigenvalues of its one-body reduced…
This work is concerned with the quantification of the epistemic uncertainties induced the discretization of partial differential equations. Following the paradigm of probabilistic numerics, we quantify this uncertainty probabilistically.…
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…
In this paper we introduce a new lifetime distribution by compounding exponential and Poisson-Lindley distributions, named exponential Poisson-Lindley distribution. Several properties are derived, such as density, failure rate, mean…
Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences…
This paper studies the asymptotic distribution of descents $\des(w)$ in a permutation $w$, and its inverse, distributed according to the Mallows measure. The Mallows measure is a non-uniform probability measure on permutations introduced to…
We study the empirical measure associated to a sample of size $n$ and modified by $N$ iterations of the raking-ratio method. This empirical measure is adjusted to match the true probability of sets in a finite partition which changes each…