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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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Poisson approximation of binomial point processes [PDF]
E3S Web of ConferencesIn the paper, we study properties of the vertex process from convex hulls generated by independent observations of a two-dimensional random vector, the distribution of which behaves like a regularly varying function near the boundary of the support of ...
Khamdamov Isakjan, Sharipova Lola
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Compound Poisson approximation for regularly varying fields with application to sequence alignment
Bernoulli, 2019 The article presents the theory of stationary regularly varying random fields. In this context, we prove a new compound Poisson approximation theorem under appropriate dependence conditions, and demonstrate a couple of effective methods for checking its ...
Bojan Basrak, Hrvoje Planinić
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Poisson approximation of subgraph counts in stochastic block models and a graphon model [PDF]
, 2015 Small subgraph counts can be used as summary statistics for large random graphs. We use the Stein-Chen method to derive Poisson approximations for the distribution of the number of subgraphs in the stochastic block model which are isomorphic to some ...
Matthew Coulson +2 more
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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 ℙ(X ⩽ (1−ε)EX) when X is the sum of dependent indicator random variables of a special form. We show that, for large deviations, this inequality is optimal
S. Janson, L. Warnke
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Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to U-statistics and stochastic geometry [PDF]
, 2014 A Poisson or a binomial process on an abstract state space and a symmetric function $f$ acting on $k$-tuples of its points are considered. They induce a point process on the target space of $f$.
Laurent Decreusefond +2 more
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Combined Neyman–Pearson chi-square: An improved approximation to the Poisson-likelihood chi-square [PDF]
Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment, 2019 We describe an approximation to the widely-used Poisson-likelihood chi-square using a linear combination of Neyman’s and Pearson’s chi-squares, namely “combined Neyman–Pearson chi-square” ( χ CNP 2 ).
X. Ji +4 more
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Evolution of Cosmic Voids in the Schrödinger-Poisson Formalism
The Open Journal of Astrophysics, 2022 We investigate the evolution of cosmic voids in the Schrödinger-Poisson formalism, finding wave mechanical solutions for the dynamics in a standard cosmological background with appropriate boundary conditions.
Aoibhinn Gallagher, Peter Coles
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Data-Driven Markov Decision Process Approximations for Personalized Hypertension Treatment Planning
MDM Policy & Practice, 2016 Background: Markov decision process (MDP) models are powerful tools. They enable the derivation of optimal treatment policies but may incur long computational times and generate decision rules that are challenging to interpret by physicians.
Greggory J. Schell PhD +4 more
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Probability Surveys, 2019 We overview results on the topic of Poisson approximation that are missed in existing surveys. The topic of Poisson approximation to the distribution of a sum of integer-valued random variables is presented as well. We do not restrict ourselves to a particular method, and overview the whole range of issues including the general limit theorem, estimates
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