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Mathematics > Statistics Theory

arXiv:2109.02538 (math)
[Submitted on 6 Sep 2021 (v1), last revised 3 Nov 2021 (this version, v2)]

Title:Bounding Means of Discrete Distributions

Authors:Eric Bax, Frédéric Ouimet
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Abstract:We introduce methods to bound the mean of a discrete distribution (or finite population) based on sample data, for random variables with a known set of possible values. In particular, the methods can be applied to categorical data with known category-based values. For small sample sizes, we show how to leverage the knowledge of the set of possible values to compute bounds that are stronger than for general random variables such as standard concentration inequalities.
Comments: 9 pages, 8 figures
Subjects: Statistics Theory (math.ST); Information Theory (cs.IT); Probability (math.PR)
MSC classes: 62G15, 62G05
Cite as: arXiv:2109.02538 [math.ST]
  (or arXiv:2109.02538v2 [math.ST] for this version)
  https://doi.org/10.48550/arXiv.2109.02538
Journal reference: IEEE International Conference on Big Data, December 15-18, 2021

Submission history

From: Frédéric Ouimet [view email]
[v1] Mon, 6 Sep 2021 15:26:35 UTC (509 KB)
[v2] Wed, 3 Nov 2021 19:32:08 UTC (511 KB)
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