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奇异 PDF 随机取样

用概率密度函数定义公式分布. 密度函数不连续且包含一个无穷奇异点.

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dist = ProbabilityDistribution[ Piecewise[{{1/(4 Sqrt[Abs[x]]), -1 < x < 0}, {2/3, 1/4 < x <= 1}}, 0], {x, -1, 1}]

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从分布中生成随机样本，并比较直方图和密度函数.

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sample = RandomVariate[dist, 10^5];

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Show[Histogram[sample, {-1, 1, 0.05}, "PDF", PlotTheme -> "Detailed"], Plot[PDF[dist, x], {x, -1, 1}, ImageSize -> Medium, PlotTheme -> "Marketing", PlotRange -> {0, 2.5}], ImageSize -> Medium]

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