公式分布的归一化

使用 ProbabilityDistribution 以及选项 Method->"Normalize" 自动计算归一化系数.

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uv\[ScriptCapitalD] = ProbabilityDistribution[Sin[x] Exp[-x], {x, 0, Pi}, Method -> "Normalize"]

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从分布取样，并比较直方图和密度函数.

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Show[Histogram[RandomVariate[uv\[ScriptCapitalD], 10^4], Automatic, PDF, PlotTheme -> "Detailed"], Plot[PDF[uv\[ScriptCapitalD], x], {x, 0, Pi}, PlotTheme -> "Marketing"], ImageSize -> Medium]

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用选项 Method->"Normalize" 归一化多元正态分布.

In[3]:=

mv\[ScriptCapitalD] = ProbabilityDistribution[Boole[x^2 + y^2 < 1], {x, 0, 1}, {y, 0, 1}, Method -> "Normalize"]

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In[4]:=

Show[Histogram3D[ RandomVariate[mv\[ScriptCapitalD], 10^4, Method -> "AcceptanceRejection"], 10, PDF, PlotTheme -> "Detailed"], Plot3D[PDF[mv\[ScriptCapitalD], {x, y}], {x, 0, 1}, {y, 0, 1}, PlotStyle -> None], ImageSize -> Medium]

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