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On the Convergence of Hypergeometric to Binomial Distributions

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  • Upul Rupassara
  • Bishnu Sedai

Abstract

This study presents a measure-theoretic approach to estimate the upper bound on the total variation of the difference between hypergeometric and binomial distributions using the Kullback-Leibler information divergence. The binomial distribution can be used to find the probabilities associated with the binomial experiments. But if the sample size is large relative to the population size, the experiment may not be binomial, and a binomial distribution is not a good choice to find the probabilities associated with the experiment. The hypergeometric probability distribution is the appropriate probability model to be used when the sample size is large compared to the population size. An upper bound for the total variation in the distance between the hypergeometric and binomial distributions is derived using only the sample and population sizes. This upper bound is used to demonstrate how the hypergeometric distribution uniformly converges to the binomial distribution when the population size increases relative to the sample size.

Suggested Citation

  • Upul Rupassara & Bishnu Sedai, 2023. "On the Convergence of Hypergeometric to Binomial Distributions," Computer and Information Science, Canadian Center of Science and Education, vol. 16(3), pages 1-15, August.
    • Handle: RePEc:ibn:cisjnl:v:16:y:2023:i:3:p:15
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    References listed on IDEAS

    as
    1. W. Vervaat, 1969. "Upper bounds for the distance in total variation between the binomial or negative binomial and the Poisson distribution," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 23(1), pages 79-86, March.
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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