Total Variation Distance of Normal Approximation for a Poisson 100.

22 Views Asked by At

Ross and Pekoz's book A Second Course in Probability gives the following question in their chapter on Stein-Chen Method:

Compute a bound on the accuracy of a normal approximation for a Poisson random variable with mean 100.

I believe this post was seeking help on the same question, but never found it Accuracy of a Normal Approximation for a Poisson random variable.

Based on the context of the text, the intention is to bound the total variation distance between the Poisson and a normal random variable that approximates it (as if by CLT). The book computes an upper bound of the form

$$2 \sqrt{ 3 \sum_{i=1}^{n} E[|X_i|^3] }$$

although this has only produced values of around 1.09 which is trivial as $d_{TV}$ is bounded above by 1. Is that the point of the problem, or is there another technique that might allow for finding a tighter bound which is just being overlooked?