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BinomialPointProcess[n,reg]

代表一个在区域 reg 中有 n 个点的二项式点过程.

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BinomialPointProcess

BinomialPointProcess[n,reg]

代表一个在区域 reg 中有 n 个点的二项式点过程.

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范例

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基本范例  (2)

对 BinomialPointProcess 抽样：

Wolfram Language code: pts = RandomPointConfiguration[BinomialPointProcess[200, Disk[]], Disk[]]
Wolfram Language code: Show[RegionPlot[pts["ObservationRegion"]], ListPlot[pts]]

对数个实现进行抽样：

Wolfram Language code: pts = RandomPointConfiguration[BinomialPointProcess[1000, Disk[]], Disk[], 3]
Wolfram Language code: pts["ConfigurationCount"]
Wolfram Language code: pts["PointCountList"]
Wolfram Language code: Show[RegionPlot[pts["ObservationRegion"]], ListPlot[pts]]

范围  (2)

从任何 RegionEmbeddingDimension 等于其 RegionDimension 的有效 RegionQ 中进行抽样：

Wolfram Language code: ℛ = ImplicitRegion[x ^ 2 - 2y ^ 2 <= 1, {{x, -3, 3}, {y, -4, 4}}];
Wolfram Language code: {RegionQ[ℛ], RegionEmbeddingDimension[ℛ] == RegionDimension[ℛ]}
Wolfram Language code: pts = RandomPointConfiguration[BinomialPointProcess[500, ℛ], ℛ]
Wolfram Language code: Show[RegionPlot[pts["ObservationRegion"]], ListPlot[pts]]

在某地理区域中创建二项点过程：

Wolfram Language code: reg = GeoDisk[Entity["City", {"Champaign", "Illinois", "UnitedStates"}], Quantity[2, "Miles"]];
Wolfram Language code: proc = BinomialPointProcess [20, reg]

在同样的区域模拟点：

Wolfram Language code: sample = RandomPointConfiguration[proc, reg]
Wolfram Language code: GeoListPlot[sample]

应用  (1)

一位射手在范围内随机对一个直径为1米的圆形目标射击12发子弹. 模拟可能的子弹路径：

Wolfram Language code: reg = Disk[]; proc = BinomialPointProcess[12, reg];
Wolfram Language code: simulations = RandomPointConfiguration[proc, reg, 4]
Wolfram Language code: Show[Region[reg], ListPlot[#, PlotStyle -> PointSize[0.03]]]& /@ simulations["PointsList"]

属性和关系  (4)

BinomialPointProcess 中的点的数量由 n 定义：

Wolfram Language code: PointCountDistribution[BinomialPointProcess[n, Disk[{0, 0}, r]]]

在单位圆盘上模拟 BinomialPointProcess：

Wolfram Language code: reg = Disk[]; proc = BinomialPointProcess[n = 100, reg];
Wolfram Language code: sample = RandomPointConfiguration[proc, reg, 500]

有边界的子集上对应的 PointCountDistribution：

Wolfram Language code: reg1 = Disk[{0, 0}, 1 / 3]; dist = PointCountDistribution[proc, reg1]

与概率分布函数比较自己种点数的直方图：

Wolfram Language code: subdata = SpatialPointData[sample, reg1]
Wolfram Language code: ns = subdata["PointCountList"];
Wolfram Language code: Show[Histogram[ns, {1}, PDF], DiscretePlot[PDF[dist, x], {x, 0, 100}, PlotStyle -> PointSize[Medium]]]

将 BinomialDistribution 拟合到点数：

Wolfram Language code: edist = EstimatedDistribution[ns, BinomialDistribution[n, a]]

检验拟合优度：

Wolfram Language code: DistributionFitTest[ns, edist, "TestConclusion"]

与理论分布比较检验：

Wolfram Language code: DistributionFitTest[ns, dist, "TestConclusion"]

区域覆盖上的 PointCountDistribution：

Wolfram Language code: reg = Rectangle[]; proc = BinomialPointProcess[100, reg];

定义一个三组覆盖：

Wolfram Language code: r1 = Rectangle[{0, 1 / 2}, {1 / 3, 1}]; r2 = RegionDifference[Disk[{0, 0}, 2 / 3, {0, π / 2}], r1];
Wolfram Language code: covering = {r1, r2, RegionDifference[reg, RegionUnion[r1, r2]]};
Wolfram Language code: Show[Table[Region[Style[covering[[i]], ColorData[97, i]]], {i, 3}]]

覆盖的点数分布：

Wolfram Language code: PointCountDistribution[proc, covering]

为二项点过程计算无类型概率：

Wolfram Language code: proc = BinomialPointProcess[100, Rectangle[{-1, -1}, {1, 1}]];
Wolfram Language code: reg1 = Disk[{0, 0}, 1 / 10];
Wolfram Language code: PDF[PointCountDistribution[proc, reg1], 0]//N

对于矩形：

Wolfram Language code: reg2 = Rectangle[{0, 0}, {.1, .1}];
Wolfram Language code: PDF[PointCountDistribution[proc, reg2], 0]//N

二项点过程为静止的——其强度有平移不变性：

Wolfram Language code: proc = BinomialPointProcess[n, Disk[{0, 0}, 100]];

子区域内的点数分布：

Wolfram Language code: subreg1 = Disk[{0, 0}, 50];
Wolfram Language code: dist1 = PointCountDistribution[proc, subreg1]

平移子区域内的点数分布：

Wolfram Language code: subreg2 = TransformedRegion[subreg1, TranslationTransform[{RandomInteger[50], RandomInteger[50]}]]
Wolfram Language code: dist2 = PointCountDistribution[proc, subreg2]
Wolfram Language code: dist1 === dist2
Wolfram Research (2020)，BinomialPointProcess，Wolfram 语言函数，https://reference.wolfram.com/language/ref/BinomialPointProcess.html.

文本

Wolfram Research (2020)，BinomialPointProcess，Wolfram 语言函数，https://reference.wolfram.com/language/ref/BinomialPointProcess.html.

CMS

Wolfram 语言. 2020. "BinomialPointProcess." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/BinomialPointProcess.html.

APA

Wolfram 语言. (2020). BinomialPointProcess. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/BinomialPointProcess.html 年

BibTeX

@misc{reference.wolfram_2026_binomialpointprocess, author="Wolfram Research", title="{BinomialPointProcess}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/BinomialPointProcess.html}", note=[Accessed: 13-July-2026]}

BibLaTeX

@online{reference.wolfram_2026_binomialpointprocess, organization={Wolfram Research}, title={BinomialPointProcess}, year={2020}, url={https://reference.wolfram.com/language/ref/BinomialPointProcess.html}, note=[Accessed: 13-July-2026]}