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,dummy = plt.hist(lognormal_values,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