numpy生成随机数组,超几何分布与连续分布

import numpy as np
import matplotlib.pyplot as plt

cash = np.zeros(10000)  # 生成10000个0的数组
cash[0] = 1000      # 数组的第一个元素设置为1000
outcome = np.random.binomial(9, 0.5, size=len(cash))
# 生成一个随机数组, 每次抛9个硬币, 每次正反面的几率为1/2, 数组长10000

for i in range(1, len(cash)):
    if outcome[i] < 5:
        cash[i] = cash[i - 1] - 1
    elif outcome[i] < 10:
        cash[i] = cash[i - 1] + 1
    else:
        raise AssertionError("Unexpected outcome" + outcome)
print(outcome.min(), outcome.max())

plt.plot(np.arange(len(cash)), cash)
plt.show

‘‘‘
假设一个罐子有26个球, 25个普通球, 1个倒霉球
每次从中取3个, 取这3个的时候是不放回的
‘‘‘

import numpy as np
import matplotlib.pyplot as plt

points = np.zeros(100)
outcome = np.random.hypergeometric(25, 1, 3, size=len(points))
# 25个普通球, 1个倒霉球, 一次取3个(不放回), 一共取len(points)次
# 取到普通球得1分, 倒霉球得0分

for i in range(len(points)):
    if outcome[i] == 3:
        points[i] = points[i - 1] + 1
    elif outcome[i] == 2:
        points[i] = points[i - 1] - 6
    else:
        print(outcome[i])
    
plt.plot(np.arange(len(points)), points)
plt.show()

import numpy as np
import matplotlib.pyplot as plt

N = 10000
normal_values = np.random.normal(size=N)

dummy, bins, dummy = plt.hist(normal_values, np.sqrt(N), normed=True, lw=1)
# 指定y轴数据源, 指定显示的小长条个数
sigma = 1
mu = 0
plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) * np.exp( - (bins - mu) ** 2 /
    (2 * sigma ** 2)), lw=2)
# 第一个参数是代表x轴的数组, 第二个参数是代表y轴的数组
# 本例中第二个参数是一个定义域为bins的映射
plt.show()

import numpy as np
import matplotlib.pyplot as plt

N = 10000
lognormal_values = np.random.lognormal(size=N)

dummy, bins, dummy = plt.hist(lognormal_values, np.sqrt(N), normed=True, lw=1)
sigma = 1
mu = 0
x = np.linspace(min(bins), max(bins), len(bins))
pdf = np.exp(-(np.log(x)-mu)**2/(2*sigma**2))/(x*sigma*np.sqrt(2*np.pi))
plt.plot(x, pdf, lw=3)
plt.show