Summary
The probability functions of the hypergeometric (Hy) and binomial (Bi) distributions are compared by means of simple majorizing functions (upper bounds) for the ratio R = Hy/Bi. After applying a suitable permutation of parameters (if necessary) R can always be kept below \( \sqrt {2} \).
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References
Abramowitz M, Stegun IA (1964) Handbook of Mathematical Functions. National Bureau of Standards, Applied Mathematics Series 55, Washington DC
Brunk HD, Holstein JE, Williams FW (1968) A Comparison of Binomial Approximations to the Hypergeometric Distribution. The American Statistician 22:24–26
Lieberman GJ, Owen DB (1961) Tables of the Hypergeometric Probability Distribution. Stanford University Press, Stanford
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© 1987 Springer-Verlag Berlin Heidelberg
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Ahrens, J.H. (1987). A Comparison of Hypergeometric Distributions with Corresponding Binomial Distributions. In: Opitz, O., Rauhut, B. (eds) Ökonomie und Mathematik. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72672-9_24
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DOI: https://doi.org/10.1007/978-3-642-72672-9_24
Publisher Name: Springer, Berlin, Heidelberg
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