numpy 概率分布

1. 二项分布

numpy.random.binomial(n, p, size=None)¶
n: 试验的次数
p: 成功的概率
size: 输出的格式
返回n次试验得到成功样本的次数

>>> np.random.binomial(10, 0.5)
4
>>> np.random.binomial(10, 0.5, 100)
array([6, 5, 7, 3, 3, 7, 7, 4, 6, 4, 3, 5, 5, 4, 4, 3, 5, 3, 6, 5, 7, 5,
       8, 1, 3, 6, 6, 6, 8, 7, 3, 3, 5, 6, 9, 4, 5, 5, 5, 6, 5, 4, 2, 4,
       3, 2, 4, 5, 3, 4, 6, 5, 5, 6, 6, 4, 5, 7, 2, 5, 5, 4, 4, 4, 2, 2,
       4, 3, 4, 5, 5, 5, 5, 5, 4, 4, 4, 9, 4, 4, 5, 4, 6, 5, 5, 5, 6, 5,
       7, 3, 3, 4, 4, 5, 4, 5, 6, 7, 4, 5])
>>> np.random.binomial(10, 0.5, (10,2))
array([[5, 4],
       [6, 5],
       [2, 7],
       [4, 7],
       [7, 5],
       [6, 4],
       [5, 5],
       [7, 8],
       [4, 5],
       [5, 4]])

2. 均匀分布

numpy.random.uniform(low=0.0, high=1.0, size=None)¶
low: [low, high), x轴的左边界
high: x轴的有边界
size: 同上
返回均匀分布抽样得到的样本

>>> np.random.uniform(-1, 0)
-0.3215569004238422
>>> np.random.uniform(1, 2)
1.6176921978063046
>>> np.random.uniform(1, 2, 10)
array([1.12308939, 1.75385708, 1.10591517, 1.68946113, 1.76664439,
       1.82339173, 1.32988529, 1.46474089, 1.26986578, 1.83440486])

3. 高斯分布(正态分布)

numpy.random.normal(loc=0.0, scale=1.0, size=None)¶
loc: 均值
scale: 标准差
size: 同上
返回正态分布的样本

>>> s = np.random.normal(0, 0.1, 1000)
>>> np.mean(s)
0.004807401973675762
>>> np.std(s)
0.09799453406363992
>>> import matplotlib.pyplot as plt
>>> plt.hist(s, 30, density=True)
(array([0.04649826, 0.        , 0.04649826, 0.        , 0.13949478,
       0.18599304, 0.37198607, 0.41848433, 0.92996518, 1.34844951,
       1.95292687, 1.62743906, 2.65040076, 3.67336245, 3.3943729 ,
       3.90585375, 4.46383285, 3.48736942, 3.85935549, 3.06888509,
       3.11538335, 1.95292687, 2.23191643, 1.39494777, 0.92996518,
       0.41848433, 0.18599304, 0.32548781, 0.18599304, 0.18599304]), array([-0.35268248, -0.3311763 , -0.30967012, -0.28816394, -0.26665776,
       -0.24515158, -0.22364539, -0.20213921, -0.18063303, -0.15912685,
       -0.13762067, -0.11611449, -0.09460831, -0.07310212, -0.05159594,
       -0.03008976, -0.00858358,  0.0129226 ,  0.03442878,  0.05593497,
        0.07744115,  0.09894733,  0.12045351,  0.14195969,  0.16346587,
        0.18497206,  0.20647824,  0.22798442,  0.2494906 ,  0.27099678,
        0.29250296]), <a list of 30 Patch objects>)
>>> plt.show()

4. 卡方分布

numpy.random.chisquare(df, size=None)¶
df: 自由度
返回取样的样本

>>> np.random.chisquare(2, 10)
array([0.57828996, 1.44692155, 1.3593016 , 5.82680881, 0.66790546,
       3.90958583, 2.58751119, 1.1587489 , 0.20344843, 8.62224483])
>>> np.random.chisquare(3, 10)
array([5.29193161, 1.49728924, 2.73340095, 2.44084495, 2.6488522 ,
       5.45728677, 6.62040015, 0.2761154 , 2.2039041 , 0.52572555])
>>> np.random.chisquare(4, 10)
array([0.65494551, 3.76197252, 2.45412806, 1.40603174, 3.99235582,
       3.47982822, 3.02089244, 3.86537378, 2.51286349, 2.03157254])

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