Related papers: A note on sums of independent random variables

Let $X_{1},\ldots ,X_{n}$ be $n$ real-valued dependent random variables. With motivation from Mitra and Resnick (2009), we derive the tail asymptotic expansion for the weighted sum of order statistics $X_{1:n}\leq \cdots \leq X_{n:n}$ of…

In this work, we propose a class of importance sampling (IS) estimators for estimating the right tail probability of a sum of continuous random variables based on a change of variables to $L^1$ polar coordinates in which the radial and…

We derive sharp probability bounds on the tails of a product of symmetric non-negative random variables using only information about their first two moments. If the covariance matrix of the random variables is known exactly, these bounds…

Let $X_1,\dots,X_n$ be independent normal random variables with $X_i\sim N(\mu_i,\sigma_i^2)$, and set $Z=\prod_{i=1}^n X_i$. We derive asymptotic approximations for the right tail probability $\mathbb{P}(Z>x)$ as $x\to\infty$. When at…

The paper studies discrete time processes and their predictability and randomness in deterministic pathwise setting, without using probabilistic assumptions on the ensemble. We suggest some approaches to quantification of randomness based…

In this paper, we obtain some results on precise large deviations for non-random and random sums of widely dependent random variables with common dominatedly varying tail distribution or consistently varying tail distribution on…

We provide bounds on the tail probabilities for simple procedures that generate random samples _without replacement_, when the probabilities of being selected need not be equal.

Correcting for skewness can result in more accurate tail probability approximations in the central limit theorem for sums of independent random variables. In this paper, we extend the theory to sums of local statistics of independent random…

This work introduces the minimax Laplace transform method, a modification of the cumulant-based matrix Laplace transform method developed in "User-friendly tail bounds for sums of random matrices" (arXiv:1004.4389v6) that yields both upper…

This article gives a formula for associated Stirling numbers of the second kind based on the moment of a sum of independent random variables having a beta distribution. From this formula we deduce, using probabilistic approaches, lower and…

The sums and maxima of weighted non-stationary random length sequences of regularly varying random variables may have the same tail and extremal indices, Markovich and Rodionov (2020). The main constraints are that there exists a unique…

Motivated by a bidimensional discrete-time risk model in insurance, we study the second-order asymptotics for two kinds of tail probabilities of the stochastic discounted value of aggregate net losses including two business lines. These are…

We provide an inequality which is a useful tool in studying both large deviation results and limit theorems for sums of random fields with "negligible" small values. In particular, the inequality covers cases of stable limits for random…

We derive the exponential as well as power decreasing tail estimations for normed sums of centered independent identical distributed (or not) random variables on the Khintchine's form. We consider arbitrary, in particular, non-Rademacher's…

In this work, we study convergence in probability and almost sure convergence for weighted partial sums of random variables that are related to the class of generalized Oppenheim expansions. It is worth noting that the random variables…

We calculate the p-the moment of the sum of n independent random variables with respect to symmetric norm in R^n. The order of growth for upper bound p/ln p obtained in ths estimate is optimal. The result extends to generalized Lorentz…

We establish several Schur-convexity type results under fixed variance for weighted sums of independent gamma random variables and obtain nonasymptotic bounds on their R\'enyi entropies. In particular, this pertains to the recent results by…

We study the large deviation probabilities of infinite weighted sums of independent random variables that have stretched exponential tails. This generalizes Kiesel and Stadtm\"uller (2000), who study the same objects under the assumption of…

We derive upper bounds for probabilities of the form $P(g(\mathbf{X})\geq t)$ using the southwest boundary (recently introduced in our previous work) $\partial_{\mathrm{SW}} Q(g^{-1}[t,\infty))$, where $Q$ is a reflection to the first…

We derive in this article the {\it lower} bound for tail of distribution for the random variables (r.v.) through a lower estimate for its moment generating functions (MGF).