Sample from a Polynomial Density
Define a multivariate formula distribution with a polynomial probability density function.
In[1]:=
![Click for copyable input](assets.en/sample-from-a-polynomial-density/In_41.png)
dist = ProbabilityDistribution[ \[FormalX]1 (1 - \[FormalX]1 (1 - \
\[FormalX]2) \[FormalX]2), {\[FormalX]1, 0, 1}, {\[FormalX]2, 0, 1},
Method -> "Normalize"]
Out[1]=
![](assets.en/sample-from-a-polynomial-density/O_35.png)
The density integrates to 1 in the given domain.
In[2]:=
![Click for copyable input](assets.en/sample-from-a-polynomial-density/In_42.png)
Integrate[PDF[dist, {x, y}], {x, 0, 1}, {y, 0, 1}]
Out[2]=
![](assets.en/sample-from-a-polynomial-density/O_36.png)
Sample from the distribution and compare the histogram with the density function.
show complete Wolfram Language input
Out[3]=
![](assets.en/sample-from-a-polynomial-density/O_37.png)