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arXiv · 2608.27143

An approximate zero bias transformation for random sums: Applications to sampling with outliers, auto insurance, and generative AI

Wasamon Jantai·Nathakhun Wiroonsri
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Abstract

We develop $L^1$ bounds for the difference between a test function of a random sum and a standard normal random variable, where the summands are assumed to be independent but not necessarily identically distributed. The bounds are obtained through a new version of the approximate zero bias transformation specifically developed for random sums. Although the identical distribution assumption is relaxed, the bounds are of order $1/\sqrt{n}$, matching the order of existing bounds in the literature under the same distributional assumption on the number of summands. The main results are then applied to three real-world settings: random sums obtained from simple random sampling with outliers, total insurance claims, and generative AI response times.

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Wasamon Jantai, Nathakhun Wiroonsri. 2026-08-27. An approximate zero bias transformation for random sums: Applications to sampling with outliers, auto insurance, and generative AI. https://arxiv.org/abs/2608.27143

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