This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

FisherHypergeometricDistribution

FisherHypergeometricDistribution
represents a Fisher noncentral hypergeometric distribution.
  • A Fisher hypergeometric distribution gives the distribution of the number of successes in n independent draws from a population of size containing successes with the odds ratio w.
Probability density function:
Cumulative distribution function:
Mean:
Probability density function:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=
 
Cumulative distribution function:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=
 
Mean:
In[1]:=
Click for copyable input
Out[1]=
Generate a set of pseudorandom numbers that are hypergeometrically distributed:
Compare its histogram to the PDF:
Distribution parameters estimation:
Estimate the distribution parameters from sample data:
Compare the density histogram of the sample with the PDF of the estimated distribution:
Different moments with closed forms as functions of parameters:
Closed form for symbolic order:
Hazard function:
Quantile function:
CDF of FisherHypergeometricDistribution is an example of a right continuous function:
An urn contains red balls of weight and blue balls of weight . With balls drawn independently, the probability of drawing a red or blue ball depends on its weight. If , , , , and , find the distribution of the number of red balls drawn:
Find the probability that at least 3 red balls were drawn:
Find the average number of red balls:
Simulate the number of red balls in 30 consecutive samples of 12:
Relationships to other distributions:
HypergeometricDistribution is a special case:
FisherHypergeometricDistribution can be obtained from two independent binomial variates conditioning on their total:
New in 8