Notes on Poisson Approximation
نویسنده
چکیده
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 within which both mean and variance can be matched, as is possible using the normal family in the classical central limit theorem. One choice is to approximate with a member of the family
منابع مشابه
On the bounds in Poisson approximation for independent geometric distributed random variables
The main purpose of this note is to establish some bounds in Poisson approximation for row-wise arrays of independent geometric distributed random variables using the operator method. Some results related to random sums of independent geometric distributed random variables are also investigated.
متن کاملApproximating Bayes Estimates by Means of the Tierney Kadane, Importance Sampling and Metropolis-Hastings within Gibbs Methods in the Poisson-Exponential Distribution: A Comparative Study
Here, we work on the problem of point estimation of the parameters of the Poisson-exponential distribution through the Bayesian and maximum likelihood methods based on complete samples. The point Bayes estimates under the symmetric squared error loss (SEL) function are approximated using three methods, namely the Tierney Kadane approximation method, the importance sampling method and the Metrop...
متن کاملA continuous approximation fitting to the discrete distributions using ODE
The probability density functions fitting to the discrete probability functions has always been needed, and very important. This paper is fitting the continuous curves which are probability density functions to the binomial probability functions, negative binomial geometrics, poisson and hypergeometric. The main key in these fittings is the use of the derivative concept and common differential ...
متن کاملNotes on Multigrid Methods
1 The model problem: 1D Possion equation. On the unit 1D domain x ∈ [0, 1], we numerically solve Poisson equation with homogeneous boundary condition ∆u = f, x(0) = x(1) = 0. (1) Discretize the domain with n cells and locate the knowns fj and unknowns uj at nodes xj = j/n = jh, j = 0, 1, . . . , n. We would like to approximate the second derivative of u using the discrete values at the nodes. U...
متن کاملMath 159 Notes: Discrete Probabilistic Methods
1. Ramsey Theory and Tournament Graphs: 1/6/14 1 2. Expectation and Variance: 1/8/14 3 3. More Uses of Variance: 1/10/14 5 4. Alterations: 1/13/14 7 5. The Lovász Local Lemma I: 1/15/14 8 6. The Lovász Local Lemma II: 1/17/14 10 7. Poisson Approximation: Jensen’s Inequality: 1/22/14 11 8. Poisson Approximation to the Binomial: 1/24/14 13 9. The Chen-Stein Method: 1/27/14 14 10. The Probabilisti...
متن کامل