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Sums of Independent Truncated Random Variables [PDF]
The Annals of Mathematical Statistics, 1957 Let $(x_{nk}), (k = 1, 2, \cdots, k_n; n = 1, 2, \cdots)$ be a double sequence of infinitesimal (i.e. $\lim_{n \rightarrow \infty} \max_{1 \leqq k \leqq k_n} P\{|x_{nk}| > \epsilon\} = 0$ for every $\epsilon > 0$) random variables such that for each $n, x_{n1}, \cdots, x_{nk_n}$ are independent.
J. M. Shapiro
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Sums of Small Powers of Independent Random Variables [PDF]
The Annals of Mathematical Statistics, 1960 Let $(x_{nk}), k = 1, 2, \cdots, k_n; n = 1, 2, \cdots$ be a double sequence of infinitesimal random variables which are rowwise independent (i.e. $\lim_{n \rightarrow \infty} \max_{1 \leqq k \leqq k_n} P(|x_{nk}| > \epsilon) = 0$ for every $\epsilon > 0$, and for each $n, x_{n1}, \cdots, x_{nk_n}$ are independent). Let $S_n = x_{n1} + \cdots + x_{nk_n}
J. M. Shapiro
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Upper-bound estimates for weighted sums satisfying Cramer’s condition
Lietuvos Matematikos Rinkinys, 2023 Let S = ω1S1 + ω2S2 + ⋯ + ωNSN. Here Sj is the sum of identically distributed random variables and ωj > 0 denotes weight. We consider the case, when Sj is the sum of independent random variables satisfying Cramer’s condition.
Vydas Čekanavičius, Aistė Elijio
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Comparing Distributions of Sums of Random Variables by Deficiency: Discrete Case
Mathematics, 2022 In the paper, we consider a new approach to the comparison of the distributions of sums of random variables. Unlike preceding works, for this purpose we use the notion of deficiency that is well known in mathematical statistics.
Vladimir E. Bening, Victor Y. Korolev
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Computation of the Distribution of the Sum of Independent Negative Binomial Random Variables
Mathematical and Computational Applications, 2023 The distribution of the sum of negative binomial random variables has a special role in insurance mathematics, actuarial sciences, and ecology. Two methods to estimate this distribution have been published: a finite-sum exact expression and a series ...
Marc Girondot, Jon Barry
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Nonuniform estimates in the approximation by the Poisson law
Lietuvos Matematikos Rinkinys, 2023 Poisson approximation for the sum of independent random variables is investigates in this paper.
Kazimieras Padvelskis
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On the Maximum Entropy of a Sum of Independent Discrete Random Variables [PDF]
Theory of Probability and its Applications, 2020 Let $ X_1, \ldots, X_n $ be independent random variables taking values in the alphabet $ \{0, 1, \ldots, r\} $, and $ S_n = \sum_{i = 1}^n X_i $. The Shepp--Olkin theorem states that, in the binary case ($ r = 1 $), the Shannon entropy of $ S_n $ is ...
Mladen Kovačević
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Concentration for multiplier empirical processes with dependent weights
AIMS Mathematics, 2023 A novel concentration inequality for the sum of independent sub-Gaussian variables with random dependent weights is introduced in statistical settings for high-dimensional data.
Huiming Zhang, Hengzhen Huang
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ON THE MAXIMUM PARTIAL SUM OF INDEPENDENT RANDOM VARIABLES [PDF]
Proceedings of the National Academy of Sciences, 1947 K. Chung
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Nuclear Engineering and Technology, 2022 Probabilistic safety assessment is widely used to quantify the risks of nuclear power plants and their uncertainties. When the lognormal distribution describes the uncertainties of basic events, the uncertainty of the top event in a fault tree is ...
Gyun Seob Song, Man Cheol Kim
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