Results 151 to 160 of about 775,098 (192)

Extending the Poisson approximation

Science, 1993
Science ; 262 ; 5132 ; 379-380 ...
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Approximating functions by their poisson transform

Information Processing Letters, 1986
When analyzing the performance of hashing algorithms, it is usually assumed that the hash function distributes the n keys randomly over the m table positions. In this exact filling model, all the m n possible arrangements are equally likely. In some cases, the analysis under this model becomes too difficult, and a Poisson filling model is used instead.
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On Large Deviations in the Poisson Approximation

Theory of Probability & Its Applications, 1994
Summary: This paper proves a general lemma comparing the behavior of probabilities of large deviations \({\mathbf P}(X \geq x)\) of a random variable \(X\) against the Poisson distribution \(1 - P(x,\lambda)\) (\(\lambda\) is the parameter of the Poisson distribution). When upper bounds are known for the factorial cumulants \(\widetilde{\Gamma}_ k (x)\)
Statulevičius, V., Aleškevičiene, A.
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Poisson Approximation

1992
Abstract The Poisson `law of small numbers' is a central principle in modern theories of reliability, insurance, and the statistics of extremes. It also has ramifications in apparently unrelated areas, such as the description of algebraic and combinatorial structures, and the distribution of prime numbers.
A D Barbour, Lars Holst, Svante Janson
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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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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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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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Square Root approximation to the Poisson Channel

2013 IEEE International Symposium on Information Theory, 2013
Starting from the Poisson model we present a channel model for optical communications, called the Square Root (SR) Channel, in which the noise is additive Gaussian with constant variance. Initially, we prove that for large peak or average power, the transmission rate of a Poisson Channel when coding and decoding methods for the SR Channel are used ...
Tsiatmas, A., Willems, F.M.J., Baggen, C.P.M.J.   +2 more
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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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COMPARISON OF APPROXIMATIONS FOR COMPOUND POISSON PROCESSES

ASTIN Bulletin, 2015
AbstractIn this paper, we compare the error in several approximation methods for the cumulative aggregate claim distribution customarily used in the collective model of insurance theory. In this model, it is usually supposed that a portfolio is at risk for a time period of length t.
Choirat, C., SERI, RAFFAELLO
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