Polynomial birth-death distribution approximation in Wasserstein distance

Details Polynomial birth-death distribution approximation in Wasserstein distance Polynomial birth-death distribution approximation in Wasserstein distance

2008-12-28

arxiv.org/abs/0812.4847v1

Journal of Theoretical Probability 22 (2009), 294--310.

Mathematics

Probability

16 pages

Scientific paper

The polynomial birth-death distribution (abbr. as PBD) on $\ci=\{0,1,2, >...\}$ or $\ci=\{0,1,2, ..., m\}$ for some finite $m$ introduced in Brown & Xia (2001) is the equilibrium distribution of the birth-death process with birth rates $\{\alpha_i\}$ and death rates $\{\beta_i\}$, where $\a_i\ge0$ and $\b_i\ge0$ are polynomial functions of $i\in\ci$. The family includes Poisson, negative binomial, binomial and hypergeometric distributions. In this paper, we give probabilistic proofs of various Stein's factors for the PBD approximation with $\a_i=a$ and $\b_i=i+bi(i-1)$ in terms of the Wasserstein distance. The paper complements the work of Brown & Xia (2001) and generalizes the work of Barbour & Xia (2006) where Poisson approximation ($b=0$) in the Wasserstein distance is investigated. As an application, we establish an upper bound for the Wasserstein distance between the PBD and Poisson binomial distribution and show that the PBD approximation to the Poisson binomial distribution is much more precise than the approximation by the Poisson or shifted Poisson distributions.

Affiliated with

Also associated with

No associations

Rating

Polynomial birth-death distribution approximation in Wasserstein distance does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Polynomial birth-death distribution approximation in Wasserstein distance, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Polynomial birth-death distribution approximation in Wasserstein distance will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-448456