hypergeometric distribution

Definitions

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

Equivalents

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.”

“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.”

CEFR level