The hypergeometric distribution
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The hypergeometric distribution describes the probability of
successes in
draws
from a finite population size
containing
successes
without replacement. This contrasts with the binomial
distribution which describes the probability of
successes
in
draws with
replacement
Distribution name
|
Hypergeometric
distribution
|
Common notation
|

|
Parameters
|
=
population size, integral ( )
=
sample size, integral ( )
=
number of tagged items, integral ( )
|
Domain
|

|
Probability mass
function
|

|
Cumulative distribution
function
|

where

is the
generalised hypergeometric function, i.e.

and involves the
rising factorial or Pochhammer notation, i.e. and 
|
Mean
|

|
Variance
|

|
Skewness
|

|
(Excess) kurtosis
|

where



|
Characteristic function
|

|
Nematrian web functions
Functions relating to the above distribution may be accessed
via the Nematrian
web function library by using a DistributionName of “hypergeometric”.
For details of other supported probability distributions see here.
NAVIGATION LINKS
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