What is "hypergeometric distribution"

n. (context probability theory statistics English) A discrete probability distribution that describes the number of successes in a sequence of n draws from a finite population without replacement.

\, | pdf = ${{{K \choose k} {{N-K} \choose {n-k}}}\over {N \choose n}}$ | cdf = $1-{{{n \choose {k+1}}{{N-n} \choose {K-k-1}}}\over {N \choose K}} \,_3F_2\!\!\left[\begin{array}{c}1,\ k+1-K,\ k+1-n \\ k+2,\ N+k+2-K-n\end{array};1\right],$ where  F is the generalized hypergeometric function | mean = $n {K\over N}$ | median = | mode = $\left \lfloor \frac{(n+1)(K+1)}{N+2} \right \rfloor$ | variance = $n{K\over N}{(N-K)\over N}{N-n\over N-1}$ | skewness = $\frac{(N-2K)(N-1)^\frac{1}{2}(N-2n)}{[nK(N-K)(N-n)]^\frac{1}{2}(N-2)}$ | kurtosis = $\left.\frac{1}{n K(N-K)(N-n)(N-2)(N-3)}\cdot\right.$ $\Big[(N-1)N^{2}\Big(N(N+1)-6K(N-K)-6n(N-n)\Big)+$ $6 n K (N-K)(N-n)(5N-6)\Big]$ | entropy = | mgf = $\frac{{N-K \choose n} \scriptstyle{\,_2F_1(-n, -K; N - K - n + 1; e^{t}) } } {{N \choose n}} \,\!$ | char = $\frac{{N-K \choose n} \scriptstyle{\,_2F_1(-n, -K; N - K - n + 1; e^{it}) }} {{N \choose n}}$ }} In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of k successes in n draws, without replacement, from a finite population of size N that contains exactly K successes, wherein each draw is either a success or a failure. In contrast, the binomial distribution describes the probability of k successes in n draws with replacement.

In statistics, the hypergeometric test uses the hypergeometric distribution to calculate the statistical significance of having drawn a specific k successes (out of n total draws) from the aforementioned population. The test is often used to identify which sub-populations are over- or under-represented in a sample. This test has a wide range of applications. For example, a marketing group could use the test to understand their customer base by testing a set of known customers for over-representation of various demographic subgroups (e.g., women, people under 30).