Wolfram 语言™

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]:=

dist = ProbabilityDistribution[ \[FormalX]1 (1 - \[FormalX]1 (1 - \ \[FormalX]2) \[FormalX]2), {\[FormalX]1, 0, 1}, {\[FormalX]2, 0, 1}, Method -> "Normalize"]

Out[1]=

密度在给定区域内积分为 1.

In[2]:=

Integrate[PDF[dist, {x, y}], {x, 0, 1}, {y, 0, 1}]

Out[2]=

从分布取样，并比较直方图与密度函数.

In[3]:=

Show[Histogram3D[RandomVariate[dist, 10^6], 40, "PDF"], Plot3D[PDF[dist, {x, y}] // Evaluate, {x, 0, 1}, {y, 0, 1}, PlotTheme -> "Marketing"], ImageSize -> Medium]

Out[3]=