Results 11 to 20 of about 1,408,791 (309)
Compound Poisson approximation
Probability Surveys, 2022 Compound Poisson approximation appears naturally in situations where one deals with a large number of rare events. In this paper, results on the topic of compound approximation to the distribution of a sum of (possibly dependent) random variables are reviewed, and a number of open problems and directions of future research are indicated.
Čekanavičius, Vydas, Novak, S. Y.
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Relaxation of monotone coupling conditions: Poisson approximation and beyond [PDF]
Journal of Applied Probability, 2017 It is well-known that assumptions of monotonicity in size-bias couplings may be used to prove simple, yet powerful, Poisson approximation results. Here we show how these assumptions may be relaxed, establishing explicit Poisson approximation bounds ...
Daly, Fraser, Johnson, Oliver
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Karpatsʹkì Matematičnì Publìkacìï, 2022 In the paper, we investigate an asymptotic behavior of the sharp upper bounds in the integral metric of deviations of the Abel-Poisson integrals from functions from the class $L^{\psi}_{\beta, 1}$.
T.V. Zhyhallo, Yu.I. Kharkevych
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Poisson approximation of the length spectrum of random surfaces [PDF]
, 2017 Multivariate Poisson approximation of the length spectrum of random surfaces is studied by means of the Chen-Stein method. This approach delivers simple and explicit error bounds in Poisson limit theorems.
Petri, Bram, Thaele, Christoph
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Journal of Theoretical ProbabilityAbstractThe problem of evaluating the accuracy of Poisson approximation to the distribution of a sum of independent integer-valued random variables has attracted a lot of attention in the past six decades. Among authors who contributed to the topic are Prokhorov, Kolmogorov, LeCam, Shorgin, Barbour, Hall, Deheuvels, Pfeifer, Roos, and many others. From
S. Novak
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The lower tail: Poisson approximation revisited [PDF]
Random Struct. Algorithms, 2014 The well-known "Janson's inequality" gives Poisson-like upper bounds for the lower tail probability \Pr(X \le (1-\eps)\E X) when X is the sum of dependent indicator random variables of a special form.
Janson, Svante, Warnke, Lutz
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Inhomogeneous random graphs, isolated vertices, and Poisson approximation [PDF]
Journal of Applied Probability, 2017 Consider a graph on randomly scattered points in an arbitrary space, with two points $x,y$ connected with probability $\phi(x,y)$. Suppose the number of points is large but the mean number of isolated points is $O(1)$.
Penrose, Mathew D.
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Stochastic Combinatorial Optimization via Poisson Approximation [PDF]
Symposium on the Theory of Computing, 2013 We study several stochastic combinatorial problems, including the expected utility maximization problem, the stochastic knapsack problem and the stochastic bin packing problem.
Li, Jian, Yuan, Wen
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Asymptotics of approximation of functions by conjugate Poisson integrals
Karpatsʹkì Matematičnì Publìkacìï, 2020 Among the actual problems of the theory of approximation of functions one should highlight a wide range of extremal problems, in particular, studying the approximation of functional classes by various linear methods of summation of the Fourier series. In
I.V. Kal'chuk +2 more
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Poisson Approximation for Dependent Trials
The Annals of Probability, 1975 Let $X_1, \cdots, X_n$ be an arbitrary sequence of dependent Bernoulli random variables with $P(X_i = 1) = 1 - P(X_i = 0) = p_i.$ This paper establishes a general method of obtaining and bounding the error in approximating the distribution of $\sum^n_{i=1} X_i$ by the Poisson distribution.
Louis H. Y. Chen
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