Poisson approximation
نویسندگان
چکیده
منابع مشابه
Compound Poisson process approximation
Compound Poisson processes are often useful as approximate models, when describing the occurrence of rare events. In this paper, we develop a method for showing how close such approximations are. Our approach is to use Stein's method directly, rather than by way of declumping and a marked Poisson process; this has conceptual advantages, but entails technical difficulties. Several applications a...
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i=1 pi ≤ max 1≤i≤n pi, (6.1) where λ := EW = ∑n i=1 pi. Clearly, if the pi’s are not all small, there may be little content in (6.1). This is to be expected, since then EW = λ and VarW = λ − ∑n i=1 p 2 i need no longer be close to one another, whereas Poisson distributions have equal mean and variance. This makes it more natural to try to find a family of distributions for the approximation wit...
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Let X be a Poisson point process and K ⊂ R d a measurable set. Construct the Voronoi cells of all points x ∈ X with respect to X, and denote by vX (K) the union of all Voronoi cells with nucleus in K. For K a compact convex set the expectation of the volume difference V (vX (K)) − V (K) and the symmetric difference V (vX (K)△K) is computed. Precise estimates for the variance of both quantities ...
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We give an overview of the Stein{Chen method for establishing Poisson approximations of various random variables. Couplings of certain variables are used to gives explicit bounds for the total variation distance between the distribution of a random variable and a Poisson variable. Some applications are given. In some cases, explicit couplings may be used to obtain good estimates; in other appli...
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We give several examples for Poisson approximation of quantities of interest in the analysis of algorithms: the distribution of node depth in a binary search tree, the distribution of the number of losers in an election algorithm and the discounted profile of a binary search tree. A simple and well-known upper bound for the total variation distance between the distribution of a sum of independe...
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ژورنال
عنوان ژورنال: Probability Surveys
سال: 2019
ISSN: 1549-5787
DOI: 10.1214/18-ps318