hypergeometric distribution

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hypergeometric distribution (plural hypergeometric distributions)

  1. (probability theory, statistics) A discrete probability distribution that describes the probability of k "successes" in a sequence of n draws without replacement from a finite population.
    • 2002, Bryan Dodson, Dennis Nolan, Reliability Engineering Handbook, QA Publishing, page 57,
      The hypergeometric distribution differs from the binomial distribution in that the random sample of n items is selected from a finite population of N items. With the hypergeometric distribution, there is no replacement. If N is large in respect to n (N>10n), the binomial distribution is a good approximation to the hypergeometric distribution.
    • 2013, Alexandr A. Borovkov, unspecified translator, Probability Theory, [2009, Alexandr A. Borovkov, Teoriya Veroyatnostei, Knizhnyi dom Librokom, 5th Edition], Springer, page 1,
      Sampling without replacement from a large population is considered, and convergence of the emerging hypergeometric distributions to the binomial one is formally proved.
    • 2014, Mark P. Silverman, A Certain Uncertainty: Nature's Random Ways, Cambridge University Press, page 99,
      Knowing that the asymptotic form approaches that of a hypergeometric distribution is not all that helpful since this is a complicated function. [] To demonstrate analytically what the figure suggests graphically, it is better to work directly with the probability function (2.1.7) than with a moment generating function or a characteristic function, neither of which is easily calculable or useful in the case of a hypergeometric distribution.

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