hypergeometric distribution

plural hypergeometric distributions

1. mathematicsA discrete probability distribution that describes the probability of k "successes" in a sequence of n draws without replacement from a finite population.

   3 more examples

   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.

   2002, Bryan Dodson, Dennis Nolan, Reliability Engineering Handbook, QA Publishing, page 57

   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.

   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.

   2014, Mark P. Silverman, A Certain Uncertainty: Nature's Random Ways, Cambridge University Press, page 99