numpy.random.Generator.negative_binomial¶

方法

random.Generator.negative_binomial(n, p, size=None)¶

从负二项分布中提取样本。

样本是从负二项分布中提取的，具有指定的参数， n 成功与 p 成功概率，其中 n 大于0且 p 在间隔（0，1）中。

参数

n浮点数或类似浮点数的数组: 分布参数，>0。
p浮点数或类似浮点数的数组: 分布的参数。必须满足0<p<=1。
sizeint或int的元组，可选: 输出形状。如果给定的形状是，例如， (m, n, k) 然后 m * n * k 取样。如果尺寸是 None （默认），如果 n 和 p 都是标量。否则， np.broadcast(n, p).size 取样。

返回

outndarray或scalar: 从参数化负二项分布中提取样本，其中每个样本等于n，即达到n次成功之前发生的失败数。

笔记

负二项分布的概率质量函数是

System Message: WARNING/2 (P（N；N，P）=\frac{\Gamma（N+N）}{N！\伽马（n）}p ^{n}（1-p）^{n}，)

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Package inputenc Error: Unicode character ） (U+FF09) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...�（n）}p ^{n}（1-p）^{n}，\end{split} ! Package inputenc Error: Unicode character ！ (U+FF01) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...�（n）}p ^{n}（1-p）^{n}，\end{split} ! Undefined control sequence. <argument> N！\� ��马（n） l.14 ...�（n）}p ^{n}（1-p）^{n}，\end{split} ! Package inputenc Error: Invalid UTF-8 byte "BC. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...�（n）}p ^{n}（1-p）^{n}，\end{split} ! Package inputenc Error: Invalid UTF-8 byte "BD. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...�（n）}p ^{n}（1-p）^{n}，\end{split} ! Package inputenc Error: Unicode character 马 (U+9A6C) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...�（n）}p ^{n}（1-p）^{n}，\end{split} ! Package inputenc Error: Unicode character （ (U+FF08) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...�（n）}p ^{n}（1-p）^{n}，\end{split} ! Package inputenc Error: Unicode character ） (U+FF09) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...�（n）}p ^{n}（1-p）^{n}，\end{split} ! Package inputenc Error: Unicode character （ (U+FF08) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...�（n）}p ^{n}（1-p）^{n}，\end{split} ! Package inputenc Error: Unicode character ） (U+FF09) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...�（n）}p ^{n}（1-p）^{n}，\end{split} ! Package inputenc Error: Unicode character ， (U+FF0C) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...�（n）}p ^{n}（1-p）^{n}，\end{split} ! Package inputenc Error: Unicode character （ (U+FF08) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...�（n）}p ^{n}（1-p）^{n}，\end{split} ! Package inputenc Error: Unicode character ； (U+FF1B) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...�（n）}p ^{n}（1-p）^{n}，\end{split} ! 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Package inputenc Error: Unicode character （ (U+FF08) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...�（n）}p ^{n}（1-p）^{n}，\end{split} ! Package inputenc Error: Unicode character ） (U+FF09) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...�（n）}p ^{n}（1-p）^{n}，\end{split} ! Package inputenc Error: Unicode character （ (U+FF08) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...�（n）}p ^{n}（1-p）^{n}，\end{split} ! Package inputenc Error: Unicode character ） (U+FF09) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...�（n）}p ^{n}（1-p）^{n}，\end{split} ! Package inputenc Error: Unicode character ， (U+FF0C) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ...�（n）}p ^{n}（1-p）^{n}，\end{split} [1] (./math.aux) ) (see the transcript file for additional information) Output written on math.dvi (1 page, 480 bytes). Transcript written on math.log.

在哪里？ $n$ 是成功的次数， $p$ 是成功的概率， $N+n$ 是试验次数，以及 $\Gamma$ 是伽马函数。什么时候？ $n$ 是一个整数， $\frac{{\Gamma(N+n)}}{{N!\Gamma(n)}} = \binom{{N+n-1}}{{N}}$ ，这是pmf中该术语更常见的形式。负二项分布给出了N次成功的N次失败的概率，最后一次试验成功。

如果一个人反复掷骰子直到第三次出现“1”，那么出现在第三次“1”之前的非“1”数的概率分布是负二项分布。

工具书类

1: 负二项式分布〉，摘自《数学世界——一个Wolfram网络资源》。http://mathworld.wolfram.com/negative二项分布.html
2: 维基百科，“负二项分布”，https://en.wikipedia.org/wiki/negative_binomial_distribution

实例

从分发中抽取样本：

一个现实世界的例子。一家公司钻探野生猫石油勘探井，每口井的成功概率估计为0.1。每口连续井成功一次的概率是多少，即钻完5口井、钻完6口井等后一次成功的概率是多少？

>>> s = np.random.default_rng().negative_binomial(1, 0.1, 100000)
>>> for i in range(1, 11): 
...    probability = sum(s<i) / 100000.
...    print(i, "wells drilled, probability of one success =", probability)

numpy.random.Generator.multivariate_normal numpy.random.Generator.noncentral_chisquare