numpy.random.power

random.power(a, size=None)

提取样本 [0, 1] 从正指数a-1的幂分布。

也称为功率函数分布。

注解

新代码应该使用 power A方法 default_rng() 请参阅 快速启动 .

参数

a浮点数或类似浮点数的数组

分布的参数。必须为非负。

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 a 是标量。否则， np.array(a).size 取样。

返回

outndarray或scalar

从参数化功率分布中提取样本。

加薪

ValueError

如果A＜1。

参见

Generator.power

应该用于新代码。

笔记

概率密度函数是

System Message: WARNING/2 (p（x；a）=a x ^ a-1，0\le x\le 1，a>0。)

latex exited with error [stdout] This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2019/dev/Debian) (preloaded format=latex) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2018-12-01> (/usr/share/texlive/texmf-dist/tex/latex/base/article.cls Document Class: article 2018/09/03 v1.4i Standard LaTeX document class (/usr/share/texlive/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty) (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty For additional information on amsmath, use the `?' option. (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty)) (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty) (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty)) (/usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty) (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty)) (/usr/share/texlive/texmf-dist/tex/latex/anyfontsize/anyfontsize.sty) (/usr/share/texlive/texmf-dist/tex/latex/tools/bm.sty) (./math.aux) (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsa.fd) (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd) ! 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 ... x ^ a-1，0\le x\le 1，a>0。\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 ... x ^ a-1，0\le x\le 1，a>0。\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 ... x ^ a-1，0\le x\le 1，a>0。\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 ... x ^ a-1，0\le x\le 1，a>0。\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 ... x ^ a-1，0\le x\le 1，a>0。\end{split} ! Package inputenc Error: Unicode character 。 (U+3002) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ... x ^ a-1，0\le x\le 1，a>0。\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 ... x ^ a-1，0\le x\le 1，a>0。\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 ... x ^ a-1，0\le x\le 1，a>0。\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 ... x ^ a-1，0\le x\le 1，a>0。\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 ... x ^ a-1，0\le x\le 1，a>0。\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 ... x ^ a-1，0\le x\le 1，a>0。\end{split} ! Package inputenc Error: Unicode character 。 (U+3002) (inputenc) not set up for use with LaTeX. See the inputenc package documentation for explanation. Type H <return> for immediate help. ... l.14 ... x ^ a-1，0\le x\le 1，a>0。\end{split} [1] (./math.aux) ) (see the transcript file for additional information) Output written on math.dvi (1 page, 416 bytes). Transcript written on math.log.

幂函数分布与帕累托分布正好相反。它也可以看作是β分布的一个特殊情况。

例如，它用于建模保险索赔的超额报告。

工具书类

1

Christian Kleiber，Samuel Kotz，“经济学和精算科学中的统计规模分布”，Wiley，2003年。

2

Heckert，N.A.和Filliben，James J.，“NIST手册148：数据图参考手册，第2卷：LET子命令和类库功能”，国家标准技术研究所手册系列，2003年6月。https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/powdpdf.pdf

实例

从分发中抽取样本：

>>> a = 5. # shape
>>> samples = 1000
>>> s = np.random.power(a, samples)

显示样本的直方图，以及概率密度函数：

>>> import matplotlib.pyplot as plt
>>> count, bins, ignored = plt.hist(s, bins=30)
>>> x = np.linspace(0, 1, 100)
>>> y = a*x**(a-1.)
>>> normed_y = samples*np.diff(bins)[0]*y
>>> plt.plot(x, normed_y)
>>> plt.show()

比较功率函数分布与帕累托的倒数。

>>> from scipy import stats 
>>> rvs = np.random.power(5, 1000000)
>>> rvsp = np.random.pareto(5, 1000000)
>>> xx = np.linspace(0,1,100)
>>> powpdf = stats.powerlaw.pdf(xx,5)  

>>> plt.figure()
>>> plt.hist(rvs, bins=50, density=True)
>>> plt.plot(xx,powpdf,'r-')  
>>> plt.title('np.random.power(5)')

>>> plt.figure()
>>> plt.hist(1./(1.+rvsp), bins=50, density=True)
>>> plt.plot(xx,powpdf,'r-')  
>>> plt.title('inverse of 1 + np.random.pareto(5)')

>>> plt.figure()
>>> plt.hist(1./(1.+rvsp), bins=50, density=True)
>>> plt.plot(xx,powpdf,'r-')  
>>> plt.title('inverse of stats.pareto(5)')

numpy.random.poisson numpy.random.rand