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Exponential bounds for the hypergeometric distribution.

Evan Greene1, Jon A Wellner2

  • 1Department of Statistics, University of Washington, Seattle, WA 98195-4322, USA.

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Summary
This summary is machine-generated.

This study provides exponential bounds for the hypergeometric distribution, incorporating a finite sampling correction. These bounds are comparable to those for the binomial distribution and extend existing convex ordering principles.

Keywords:
binomial distributionconvex orderingexponential boundfinite sampling correction factorhypergeometric distributionsampling without replacement

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Area of Science:

  • Probability theory
  • Statistical analysis

Background:

  • Existing bounds for binomial distribution by León and Perron, and Talagrand.
  • Kemperman's convex ordering for sampling without replacement.

Purpose of the Study:

  • Establish exponential bounds for the hypergeometric distribution.
  • Incorporate a finite sampling correction factor.
  • Extend Kemperman's convex ordering.

Main Methods:

  • Derivation of exponential bounds.
  • Application of convex ordering principles.
  • Analysis of sampling without replacement.

Main Results:

  • New exponential bounds for hypergeometric distribution established.
  • Finite sampling correction factor included in bounds.
  • Convex ordering extended to populations of real numbers (0, 1).

Conclusions:

  • The derived bounds offer improved accuracy for hypergeometric probabilities.
  • The extreme case of the extended convex ordering corresponds to a hypergeometric distribution.
  • Findings contribute to a deeper understanding of sampling distributions.