Normal Approximation of Poisson Functionals in Kolmogorov Distance

Stein’s method and normal approximation of Poisson functionals

Compound Poisson Approximation via Information Functionals

An information-theoretic development is given for the problem of compound Poisson approximation, which parallels earlier treatments for Gaussian and Poisson approximation. Nonasymptotic bounds are derived for the distance between the distribution of a sum of independent integervalued random variables and an appropriately chosen compound Poisson law. In the case where all summands have the same ...

On Stein’s factors for Poisson approximation in Wasserstein distance

In this note, we provide a probabilistic proof of various Stein’s factors for Poisson approximation in terms of the Wasserstein distance.

Characterizations of Multivariate Normal-Poisson Model

‎Multivariate normal-Poisson model has been recently introduced as a special case of normal stable Tweedie models‎. ‎The model is composed of a univariate Poisson variable‎, ‎and the remaining variables given the Poisson one are independent Gaussian variables with variance the value of the Poisson component‎. ‎Two characterizations of this model are shown‎, ‎...

A refinement of normal approximation to Poisson binomial

Let X1,X2, . . . ,Xn be independent Bernoulli random variables with P(Xj = 1) = 1 − P(Xj = 0)= pj and let Sn := X1 +X2 + ···+Xn. Sn is called a Poisson binomial random variable and it is well known that the distribution of a Poisson binomial random variable can be approximated by the standard normal distribution. In this paper, we use Taylor’s formula to improve the approximation by adding some...