从多项式密度中取样
定义一个有多项式概率密度函数的多元公式分布.
In[1]:=
![Click for copyable input](assets.zh/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.zh/sample-from-a-polynomial-density/O_35.png)
密度在给定区域内积分为 1.
In[2]:=
![Click for copyable input](assets.zh/sample-from-a-polynomial-density/In_42.png)
Integrate[PDF[dist, {x, y}], {x, 0, 1}, {y, 0, 1}]
Out[2]=
![](assets.zh/sample-from-a-polynomial-density/O_36.png)
从分布取样,并比较直方图与密度函数.
显示完整的 Wolfram 语言输入
Out[3]=
![](assets.zh/sample-from-a-polynomial-density/O_37.png)