Results 201 to 210 of about 249,986 (237)

Approximation by the Compound Poisson Law

Theory of Probability & Its Applications, 2005
Summary: We consider a specification of the convergence of distributions of sums of independent, nonnegative integer random variables to the compound Poisson distribution. Theorems of large deviations and asymptotic expansions under some weak conditions are proved.
Aleškevičiėnė, A. K., Statulevičius, V. A.   +1 more
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Large deviations by poisson approximations

Journal of Statistical Planning and Inference, 1992
Some sharp large deviation asymptotics are established for sums of independent, not necessarily identically distributed Bernoulli random variables. As usual, associated (Bernoulli) random variables are introduced via exponential centering. But instead of using a central limit type argument for the latter, a sharper Poisson approximation is applied here.
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Fisher Information, Compound Poisson Approximation, and the Poisson Channel

2007 IEEE International Symposium on Information Theory, 2007
Fisher information plays a fundamental role in the analysis of Gaussian noise channels and in the study of Gaussian approximations in probability and statistics. For discrete random variables, the scaled Fisher information plays an analogous role in the context of Poisson approximation.
Madiman, M, Johnson, OT, Kontoyiannis, I
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On the poisson approximation to the multinomial distribution

Canadian Journal of Statistics, 1980
AbstractLet Xi be the number of outcomes in class Ci, i = 0,…,k, during n independent possibly non‐identical trials. If class C0 has high probability we show {Xi}ki=1 can be approximated by {Yi}ki=1 a sequence of independent Poisson random variables with ℰXi=ℰYi. A bound on the error is given.
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Poisson approximation for large deviations

Random Structures & Algorithms, 1990
AbstractUpper and lower bounds are given for P(S ≤ k), 0 ≤ k ≤ ES, where S is a sum of indicator variables with a special structure, which appears, for example, in subgraph counts in random graphs. in typical cases, these bounds are close to the corresponding probabilities for a Poisson distribution with the same mean as S.
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Properties of the interrupted poisson approximation

Operations Research Letters, 1984
The interrupted Poisson approximation has been used very successfully for overflow systems. The approximation is fitted to the overflow stream so that if the number of overflow servers was infinite the distribution of the number of serves in use would have the same first three moments. The approximation is shown to be a lower bound in the sense that it
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On approximation by a poisson type convolution

Lithuanian Mathematical Journal, 1996
Consider sums \(S_n\) of independent, identically distributed random variables \(X_j\) having a lattice distribution concentrated on \(\{0,1,2,\dots\}\). The author uses Poisson type convolutions to approximate the probabilities \(P(S_n= k)\) in a general setting.
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Poisson approximation

Proceedings Geometric Modeling and Processing 2000. Theory and Applications, 2000
Ronald N. Goldman, Géraldine Morin
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Poisson Approximations and the Definition of the Poisson Process

The American Mathematical Monthly, 1984
On donne certains resultats concernant l'erreur d'approximation de certaines variables aleatoires par des distributions de Poisson.
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Poisson Approximation

Bulletin of the London Mathematical Society, 1993
Rudolf Grubel, A. D. Barbour, Lars Holst, Svante Janson   +3 more
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