相关论文: A note on a variance bound for the multinomial and…

The upper extremes of a Markov chain with regulary varying stationary marginal distribution are known to exhibit under general conditions a multiplicative random walk structure called the tail chain. More generally, if the Markov chain is…

Categorical random variables are a common staple in machine learning methods and other applications across disciplines. Many times, correlation within categorical predictors exists, and has been noted to have an effect on various algorithm…

We improve the previuosly known bound for some vertex Folkman numbers.

We propose a multivariate probability distribution for categorical and ordinal random variables. To this end, we use the Grassmann distribution in conjunction with dummy encoding of categorical and ordinal variables. To realize the…

We prove that for a large class of multiplicative functions, referred to as generalized divisor functions, it is possible to find a lower bound for the corresponding variance in arithmetic progressions. As a main corollary, we deduce such a…

We discuss the (twisted) weak positivity theorem. We also treat some applications.

The negative binomial distribution (NBD) has been theorized to express a scale-invariant property of many-body systems and has been consistently shown to outperform other statistical models in both describing the multiplicity of…

We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guaranteed dwell-time) as from above. The upper bounds make this…

We consider a boundary value problem involving conformable derivative of order $\alpha ,$ $1<\alpha <2$ and Dirichlet conditions. To prove the existence of solutions, we apply the method of upper and lower solutions together with Schauder's…

We derive upper bounds on the tail conditional expectation of binomial and Poisson random variables. Those upper bounds are subsequently employed to the problem of obtaining non-asymptotic lower bounds on the probability that the…

Two sharp Chernoff type inequalities are obtained for star body in $\mathbb{R}^2$, one of which is an extension of the dual Chernoff-Ou-Pan inequality, and the other is the reverse Chernoff type inequality. Furthermore, we establish a…

Sufficient oscillation conditions involving $\limsup $ and $\liminf $ for first-order differential equations with several non-monotone deviating arguments and nonnegative coefficients are obtained. The results are based on the iterative…

We derive simple but nearly tight upper and lower bounds for the binomial lower tail probability (with straightforward generalization to the upper tail probability) that apply to the whole parameter regime. These bounds are easy to compute…

We use some properties of orthogonal polynomials to provide a class of upper/lower variance bounds for a function $g(X)$ of an absolutely continuous random variable $X$, in terms of the derivatives of $g$ up to some order. The new bounds…

This note provides a Lefschetz theorem for Minkowski sums of polytopes, and conclude lower bound theorems for Minkowski sums of polytopes. It is written as an appendix to arXiv:1405.7368, so notation and references follow that paper.

We show somewhat unexpectedly that whenever a general Bernstein-type maximal inequality holds for partial sums of a sequence of random variables, a maximal form of the inequality is also valid.

In this note we prove a weighted version of the Khintchine inequalities.

Higher order Bernstein- and Markov-type inequalities are established for trigonometric polynomials on compact subsets of the real line and algebraic polynomials on compact subsets of the unit circle. In the case of Markov-type inequalities…

It is shown that simple extension of the modified negative binomial distribution describes negatively charged particle multiplicity distributions in e+e- annihilation, measured in the whole phase space, as well as the modified negative…

We obtain variance inequalities for quadratic forms of weakly dependent random variables with bounded fourth moments. We also discuss two application. Namely, we use these inequalities for deriving the limiting spectral distribution of a…