hypergeometric distribution について

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).
==Definition==
The following conditions characterize the hypergeometric distribution:
* The result of each draw (the elements of the population being sampled) can be classified into one of two mutually exclusive categories (e.g. Pass/Fail or Female/Male or Employed/Unemployed).
* The probability of a success changes on each draw, as each draw decreases the population (''sampling without replacement'' from a finite population).
A random variable

X

follows the hypergeometric distribution if its probability mass function (pmf) is given by
:

P(X = k) = \frac \binom}}

,
where
*

N

is the population size,
*

K

is the number of success states in the population,
*

n

is the number of draws,
*

k

is the number of observed successes,
*

\textstyle

is a binomial coefficient.
The pmf is positive when

\max(0, n+K-N) \leq k \leq \min(K,n)

.
The pmf satisfies the recurrence relation
:

(k + 1) (N - K - (n - k - 1)) P(X = k + 1) = (K - k) (n - k) P(X = k)

with
:

P(X = 0) = \frac}}

.

抄文引用元・出典: フリー百科事典『ウィキペディア（Wikipedia）』
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