Related papers: A lower bound on the probability that a binomial r…

We present a new inductive rule for verifying lower bounds on expected values of random variables after execution of probabilistic loops as well as on their expected runtimes. Our rule is simple in the sense that loop body semantics need to…

We derive new upper and lower bounds for probabilities that $r$ or at least $r$ from $n$ events occur. These bounds can turn to equalities. The method is discussed as well. It works for measurable space and measures with sign, too. We also…

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…

Known Bernstein-type upper bounds on the tail probabilities for sums of independent zero-mean sub-exponential random variables are improved in several ways at once. The new upper bounds have a certain optimality property.

Consider the probability that a binomial random variable Bi$(n,m/n)$ with integer expectation $m$ is at most its expectation. Chv\'atal conjectured that for any given $n$, this probability is smallest when $m$ is the integer closest to…

We present a new method to propagate lower bounds on conditional probability distributions in conventional Bayesian networks. Our method guarantees to provide outer approximations of the exact lower bounds. A key advantage is that we can…

We establish upper and lower bounds with matching leading terms for tails of weighted sums of two-sided exponential random variables. This extends Janson's recent results for one-sided exponentials.

We re-examine a lower-tail upper bound for the random variable $$X=\prod_{i=1}^{\infty}\min\left\{\sum_{k=1}^iE_k,1\right\},$$ where $E_1,E_2,\ldots\stackrel{iid}\sim\text{Exp}(1)$. This bound has found use in root-finding and seed-finding…

We give an elementary probabilistic proof of a binomial identity. The proof is obtained by computing the probability of a certain event in two different ways, yielding two different expressions for the same quantity.

In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random…

In this paper, we compute the tightest possible bounds on the probability that the optimal value of a combinatorial optimization problem in maximization form with a random objective exceeds a given number, assuming only knowledge of the…

We show that the probability that a multilinear polynomial $f$ of independent random variables exceeds its mean by $\lambda$ is at most $e^{-\lambda^2 / (R^q Var(f))}$ for sufficiently small $\lambda$, where $R$ is an absolute constant.…

We address the problem of producing a lower bound for the mean of a discrete probability distribution, with known support over a finite set of real numbers, from an iid sample of that distribution. Up to a constant, this is equivalent to…

We consider the limiting distribution of the quantity $X^s/(X+Y)^r$, where $X$ and $Y$ are two independent Binomial random variables with a common success probability and a number of trials $n$ and $m$, respectively, and $r,s$ are positive…

In this paper, we establish a fundamental connection between binomial parameters and means of bounded random variables. Such connection finds applications in statistical inference of means of bounded variables.

We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of $n$ jointly distributed random variables. We control the expectation of a randomly selected random variable from $n$ jointly…

In this paper, we consider Bayesian point estimation and predictive density estimation in the binomial case. After presenting preliminary results on these problems, we compare the risk functions of the Bayes estimators based on the…

We obtain a new upper bound for binary sums with multiplicative characters over variables belong to some sets, having small additive doubling.

This paper provides a general technique for lower bounding the Bayes risk of statistical estimation, applicable to arbitrary loss functions and arbitrary prior distributions. A lower bound on the Bayes risk not only serves as a lower bound…

We generalise the known fact that for binomial $X_{n,k} \sim \mathrm{Bin}(n, k/n)$ one has $\inf_{k>1,n} \mathrm{P}(X_{n,k} \geq k) \geq \lim_{k \to 1+}\mathrm{P}(X_{2,k} \geq k) = 1/4$ to cover probabilities of exceeding a constant shift…