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Binomial and Poisson Random Variables

2001
Before stating the fundamental principle of counting we give an example. Example 1. Assume that a restaurant offers five different specials and for each one of them you can pick either a salad or a soup. How many choices do you have? In this simple example we can just enumerate all the possibilities.
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Poisson Approximation for a Sum of Negative Binomial Random Variables

Bulletin of the Malaysian Mathematical Sciences Society, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Compound Poisson approximations for sums of 1-dependent random variables. I

Lithuanian Mathematical Journal, 2010
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Petrauskienė, J., Čekanavičius, V.
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Large Deviation Principle for Poisson Random Variables and Young Diagrams

Problems of Information Transmission, 2001
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Perfect simulation for correlated Poisson random variables conditioned to be positive

Statistics and Computing, 2002
In this paper we present a perfect simulation method for obtaining perfect samples from collections of correlated Poisson random variables conditioned to be positive. We show how to use this method to produce a perfect sample from a Boolean model conditioned to cover a set of points: in W.S. Kendall and E. Thonnes (Pattern Recognition 32(9): 1569–1586,
Yuzhi Cai, Wilfrid S. Kendall
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Poisson approximation for sums of dependent Bernoulli random variables

2006
Summary: We use the Stein-Chen method to determine a non-uniform bound for approximating the distribution of sums of dependent Bernoulli random variables by Poisson distribution. We give two formulas of non-uniform bounds and their applications.
Teerapabolarn, Al-Kanint   +1 more
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Bounds in poisson approximation for random sums of Bernoulli random variables

Let X[subscript n] be a sequence of Bernoulli random variables and a positive integer-valued random variable. Define S[subscript N] = X₁ +X₂ +… X [subscript n]) be random sums. Assume N, X₁, X₂, … are independent. In this thesis, we establish uniform and non-uniform bounds in Poisson approximation for S[subscript N]
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