PreprintCC BY 4.0arXiv
An approximate zero bias transformation for random sums: Applications to sampling with outliers, auto insurance, and generative AI
Abstract
We develop L1 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/√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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BibTeX
@misc{jantai2026approximate,
title = {{An approximate zero bias transformation for random sums: Applications to sampling with outliers, auto insurance, and generative AI}},
author = {Wasamon Jantai and Nathakhun Wiroonsri},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.27143},
eprint = {2608.27143},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27143},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An approximate zero bias transformation for random sums: Applications to sampling with outliers, auto insurance, and generative AI
AU - Wasamon Jantai
AU - Nathakhun Wiroonsri
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2608.27143
UR - https://arxiv.org/abs/2608.27143
AB - 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/√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.
ER -