numpy.random.Generator.laplace¶

方法

random.Generator.laplace(loc=0.0, scale=1.0, size=None)¶

从拉普拉斯或双指数分布中提取具有指定位置（或平均值）和刻度（衰减）的样本。

拉普拉斯分布类似于高斯/正态分布，但在峰值处更明显，尾部更粗。它表示两个独立的、相同分布的指数随机变量之间的差异。

参数

loc浮点数或类似浮点数的数组，可选: 位置， $\mu$ ，分布峰。默认值为0。
scale浮点数或类似浮点数的数组，可选: $\lambda$ ，指数衰减。默认值为1。必须是非负的。
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 loc 和 scale 都是标量。否则， np.broadcast(loc, scale).size 取样。

返回

outndarray或scalar: 从参数化拉普拉斯分布中提取样本。

笔记

它有概率密度函数

System Message: WARNING/2 (f（x；\mu，\lambda）=\frac{1}{2\lambda})

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1774年拉普拉斯第一定律指出，误差的频率可以表示为误差绝对大小的指数函数，从而得出拉普拉斯分布。对于经济学和卫生科学中的许多问题，这种分布似乎比标准高斯分布更好地模拟数据。

工具书类

1: Abramowitz，M.和Stegun，I.A.（编辑）。《数学函数与公式、图表和数学表手册》，第9版，纽约：多佛，1972年。
2: Kotz、Samuel等。”拉普拉斯分布和推广“，Birkhauser，2001.
3: 拉普拉斯分布〉，摘自《数学世界——沃尔夫拉姆网络资源》。http://mathworld.wolfram.com/laplacedistribution.html
4: 维基百科，“拉普拉斯分布”，https://en.wikipedia.org/wiki/laplace_distribution

实例

从分发中提取样本

>>> loc, scale = 0., 1.
>>> s = np.random.default_rng().laplace(loc, scale, 1000)

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, 30, density=True)
>>> x = np.arange(-8., 8., .01)
>>> pdf = np.exp(-abs(x-loc)/scale)/(2.*scale)
>>> plt.plot(x, pdf)

绘制高斯图进行比较：

>>> g = (1/(scale * np.sqrt(2 * np.pi)) *
...      np.exp(-(x - loc)**2 / (2 * scale**2)))
>>> plt.plot(x,g)

../../../_images/numpy-random-Generator-laplace-1.png

numpy.random.Generator.hypergeometric numpy.random.Generator.logistic