AN IMPROVED POISSON APPROXIMATION FOR BERNOULLI RANDOM SUMMANDS

Poisson Approximation for Sums of Dependent Bernoulli Random Variables

In this paper, 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.

Poisson Approximation for Unbounded Functions, I: Independent Summands

Let $X_{n1},\cdots,X_{nn},\ n\geq1$, be independent random variables with $P(X_{ni}=1)=1-P(X_{ni}=0)=p_{ni}$ such that $\max\{p_{ni}\colon1\leq i\leq n\}\to0$ as $n\to\infty$. Let $W_n=\sum_{1\leq k\leq n}X_{nk}$ and let $Z$ be a Poisson random variable with mean $\lambda=EW_n$. We obtain an absolute constant bound on $P(W_n=r)/P(Z=r),\ r=0,1,\cdots$, and using this, prove two Poisson approxima...

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.

Poisson approximation for non-backtracking random walks

Random walks on expander graphs were thoroughly studied, with the important motivation that, under some natural conditions, these walks mix quickly and provide an efficient method of sampling the vertices of a graph. The authors of [3] studied non-backtracking random walks on regular graphs, and showed that their mixing rate may be up to twice as fast as that of the simple random walk. As an ap...

How to Find an Extra Head: Optimal Random Shifts of Bernoulli and Poisson Random Fields