numpy.random.RandomState.weibull¶

方法

random.RandomState.weibull(a, size=None)¶

从威布尔分布中提取样本。

从具有给定形状参数的单参数威布尔分布中提取样本 a .

System Message: WARNING/2 (x=（-ln（u））^ 1/a)

这里，u是从（0,1）上的均匀分布中得出的。

更常见的2参数威布尔，包括一个尺度参数 $\lambda$ 只是 $X = \lambda(-ln(U))^{{1/a}}$ .

注解

新代码应该使用 weibull 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: 分布的形状参数。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: 从参数化威布尔分布中提取样本。

参见

scipy.stats.weibull_max
scipy.stats.weibull_min
scipy.stats.genextreme
gumbel
Generator.weibull: 应该用于新代码。

笔记

威布尔（或最小值的III型渐近极值分布、SEV III型或Rosin-Rammler分布）是一类用于建模极值问题的广义极值（GEV）分布之一。这个类包括gumbel和frechet分布。

威布尔分布的概率密度是

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在哪里？ $a$ 是形状和 $\lambda$ 规模。

函数的峰值（模式）为 $\lambda(\frac{{a-1}}{{a}})^{{1/a}}$ .

什么时候？ a = 1 威布尔分布降为指数分布。

工具书类

1: Waloddi Weibull，斯德哥尔摩皇家技术大学，1939年，“材料强度的统计理论”，Ingeniorsvetenskapasakademiens Handlingar第151号，1939年，斯德哥尔摩，Stabens Litografiska Anstalts将军。
2: Waloddi-Weibull，“广泛适用的统计分布函数”，《应用力学杂志》ASME论文1951。
3: 维基百科，“威布尔分布”，https://en.wikipedia.org/wiki/weibull_distribution

实例

从分发中抽取样本：

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

显示样本的直方图，以及概率密度函数：

>>> import matplotlib.pyplot as plt
>>> x = np.arange(1,100.)/50.
>>> def weib(x,n,a):
...     return (a / n) * (x / n)**(a - 1) * np.exp(-(x / n)**a)

>>> count, bins, ignored = plt.hist(np.random.weibull(5.,1000))
>>> x = np.arange(1,100.)/50.
>>> scale = count.max()/weib(x, 1., 5.).max()
>>> plt.plot(x, weib(x, 1., 5.)*scale)
>>> plt.show()

../../../_images/numpy-random-RandomState-weibull-1.png

numpy.random.RandomState.wald numpy.random.RandomState.zipf