二项分布
numpy.random.binomial(n, p, size=None)
#Draw samples from a binomial distribution.
#表示对一个二项分布进行采样，size表示采样的次数，n表示做了n重伯努利试验，p表示成功的概率，函数的返回值表示n中成功的次数。【例】野外正在进行9（n=9）口石油勘探井的发掘工作，每一口井能够开发出油的概率是0.1（p=0.1）。请问，最终所有的勘探井都勘探失败的概率？
import numpy as np
import matplotlib.pyplot as plt
from scipy import stats
np.random.seed(20200605)
n = 9# 做某件事情的次数
p = 0.1# 做某件事情成功的概率
size = 50000
x = np.random.binomial(n, p, size)
print(np.sum(x == 0) / size) # 0.3897【例】模拟投硬币，投2次，请问两次都为正面的概率？
import numpy as np
from scipy import stats
import matplotlib.pyplot as plt
np.random.seed(20200605)
n = 2# 做某件事情的次数,这里是投两次硬币
p = 0.5#做某件事情成功的概率，在这里即投硬币为正面的概率
size = 50000
x = np.random.binomial(n, p, size)
print(np.sum(x == 2) / size) # 0.24972泊松分布
numpy.random.poisson(lam=1.0, size=None)
#Draw samples from a Poisson distribution.
#表示对一个泊松分布进行采样，size表示采样的次数，lam表示一个单位内发生事件的平均值，函数的返回值表示一个单位内事件发生的次数。【例】假定某航空公司预定票处平均每小时接到42次订票电话，那么10分钟内恰好接到6次电话的概率是多少？
import numpy as np
from scipy import stats
import matplotlib.pyplot as plt
np.random.seed(20200605)
lam = 42 / 6# 平均值：平均每十分钟接到42/6次订票电话
size = 50000
x = np.random.poisson(lam, size)
print(np.sum(x == 6) / size) # 0.14988或者
#用poisson.pmf(k, mu)求对应分布的概率:概率质量函数 (PMF)
x = stats.poisson.pmf(6, lam)
print(x) # 0.14900277967433773超几何分布
numpy.random.hypergeometric(ngood, nbad, nsample, size=None)
#Draw samples from a Hypergeometric distribution.
#表示对一个超几何分布进行采样，size表示采样的次数，ngood表示总体中具有成功标志的元素个数，
#nbad表示总体中不具有成功标志的元素个数，ngood+nbad表示总体样本容量，
#nsample表示抽取元素的次数（小于或等于总体样本容量），
#函数的返回值表示抽取nsample个元素中具有成功标识的元素个数。【例】一共20只动物里有7只是狗，抽取12只有3只狗的概率（无放回抽样）。
import numpy as np
from scipy import stats
import matplotlib.pyplot as plt
np.random.seed(20200605)
size = 500000
x = np.random.hypergeometric(ngood=7, nbad=13, nsample=12, size=size)
'''或者
#用rvs(M, n, N, loc=0, size=1, random_state=None)模拟
x = stats.hypergeom.rvs(M=20,n=7,N=12,size=size)
'''
print(np.sum(x == 3) / size) # 0.198664均匀分布
numpy.random.uniform(low=0.0, high=1.0, size=None)
#Draw samples from a uniform distribution.
#Samples are uniformly distributed over the half-open interval [low, high) (includes low, but excludes high).
# In other words, any value within the given interval is equally likely to be drawn by uniform.【例】在low到high范围内，创建大小为size的均匀分布的随机数。
import numpy as np
import matplotlib.pyplot as plt
from scipy import stats
np.random.seed(20200614)
a = 0
b = 100
size = 50000
x = np.random.uniform(a, b, size=size)rand()是uniform()的特列，可以得到[0,1)之间的均匀分布的随机数。
numpy.random.rand(d0, d1, ..., dn)
#Random values in a given shape.
#Create an array of the given shape and populate it with random samples from a uniform distribution over [0, 1).【例】根据指定大小产生[0,1)之间均匀分布的随机数。
import numpy as np
np.random.seed(20200614)
print(np.random.rand())
# 0.7594819171852776
print(np.random.rand(5))
# [0.75165827 0.16552651 0.0538581 0.46671446 0.89076925]
print(np.random.rand(4, 3))
# [[0.10073292 0.14624784 0.40273923]
# [0.21844459 0.22226682 0.37246217]
# [0.50334257 0.01714939 0.47780388]
# [0.08755349 0.86500477 0.70566398]]
np.random.seed(20200614)
print(np.random.uniform()) # 0.7594819171852776
print(np.random.uniform(size=5))
# [0.75165827 0.16552651 0.0538581 0.46671446 0.89076925]
print(np.random.uniform(size=(4, 3)))
# [[0.10073292 0.14624784 0.40273923]
# [0.21844459 0.22226682 0.37246217]
# [0.50334257 0.01714939 0.47780388]
# [0.08755349 0.86500477 0.70566398]]randint()是uniform的另一特例，可以得到[low,high)之间均匀分布的随机整数。
numpy.random.randint(low, high=None, size=None, dtype='l') Return random integers from low (inclusive) to high (exclusive).
Return random integers from the “discrete uniform” distribution of the specified dtype in the “half-open” interval [low, high). If high is None (the default), then results are from [0, low).【例】若high不为None时，取[low,high)之间随机整数，否则取值[0,low)之间随机整数。
import numpy as np
np.random.seed(20200614)
x = np.random.randint(2, size=10)
print(x)
# [0 0 0 1 0 1 0 0 0 0]
x = np.random.randint(1, size=10)
print(x)
# [0 0 0 0 0 0 0 0 0 0]
x = np.random.randint(5, size=(2, 4))
print(x)
# [[3 3 0 1]
# [1 1 0 1]]
x = np.random.randint(1, 10, [3, 4])
print(x)
# [[2 1 7 7]
# [7 2 4 6]
# [8 7 2 8]]正态分布
标准正态分布
numpy.random.randn(d0, d1, ..., dn)
#Return a sample (or samples) from the "standard normal" distribution.【例】根据指定大小产生满足标准正态分布的数组（均值为0，标准差为1）。
import numpy as np
import matplotlib.pyplot as plt
from scipy import stats
np.random.seed(20200614)
size = 50000
x = np.random.randn(size)指定分布以及所需参数来进行随机，例如高斯分布中的mu和sigma。
numpy.random.normal(loc=0.0, scale=1.0, size=None)
#Draw random samples from a normal (Gaussian) distribution.
#normal()为创建均值为 loc（mu），标准差为 scale（sigma），大小为 size 的数组。import matplotlib.pyplot as plt
np.random.seed(20200614)
x = 0.5 * np.random.randn(2, 4) + 5
'''或者
#模拟10000个随机变量
x = 0.5*stats.norm.rvs(size=(2,4))+5
'''
print(x)
# [[5.39654234 5.4088702 5.49104652 4.95817289]
# [4.31977933 4.76502391 4.70720327 4.36239023]]
np.random.seed(20200614)
mu = 5#平均值
sigma = 0.5#标准差
x = np.random.normal(mu, sigma, (2, 4))
print(x)
# [[5.39654234 5.4088702 5.49104652 4.95817289]
# [4.31977933 4.76502391 4.70720327 4.36239023]]
size = 50000
x = np.random.normal(mu, sigma, size)
print(np.mean(x)) # 4.996403463175092
print(np.std(x, ddof=1)) # 0.4986846716715106（#样本标准差）指数分布
numpy.random.exponential(scale=1.0, size=None)
#Draw samples from an exponential distribution.import numpy as np
import matplotlib.pyplot as plt
from scipy import stats
np.random.seed(20200614)
lam = 7
size = 50000
x = np.random.exponential(1 / lam, size)随机从序列中获取元素
numpy.random.choice(a, size=None, replace=True, p=None)
@Generates a random sample from a given 1-D array.
#从序列中获取元素，若a为整数，元素取值从np.range(a)中随机获取；若a为数组，取值从a数组元素中随机获取。
#该函数还可以控制生成数组中的元素是否重复replace，以及选取元素的概率p。import numpy as np
np.random.seed(20200614)
x = np.random.choice(10, 3)
print(x) # [2 0 1]
x = np.random.choice(10, 3, p=[0.05, 0, 0.05, 0.9, 0, 0, 0, 0, 0, 0])
print(x) # [3 2 3]
x = np.random.choice(10, 3, replace=False, p=[0.05, 0, 0.05, 0.9, 0, 0, 0, 0, 0, 0])
print(x) # [3 0 2]
aa_milne_arr = ['pooh', 'rabbit', 'piglet', 'Christopher']
x = np.random.choice(aa_milne_arr, 5, p=[0.5, 0.1, 0.1, 0.3])
print(x) # ['pooh' 'rabbit' 'pooh' 'pooh' 'pooh']
np.random.seed(20200614)
x = np.random.randint(0, 10, 3)
print(x) # [2 0 1]对数据集进行洗牌操作
numpy.random.shuffle(x)
#Modify a sequence in-place by shuffling its contents.
#This function only shuffles the array along the first axis of a multi-dimensional array.
#The order of sub-arrays is changed but their contents remains the same.
#对x进行重排序，如果x为多维数组，只沿第 0 轴洗牌，改变原来的数组，输出为None。import numpy as np
np.random.seed(20200614)
x = np.arange(20).reshape((5, 4))
print(x)
# [[ 0 1 2 3]
# [ 4 5 6 7]
# [ 8 9 10 11]
# [12 13 14 15]
# [16 17 18 19]]
np.random.shuffle(x)
print(x)
# [[ 4 5 6 7]
# [ 0 1 2 3]
# [ 8 9 10 11]
# [16 17 18 19]
# [12 13 14 15]]另一种洗牌操作
numpy.random.permutation(x)
#Randomly permute a sequence, or return a permuted range.
#If x is a multi-dimensional array, it is only shuffled along its first index.
#permutation()函数的作用与shuffle()函数相同，可以打乱第0轴的数据，但是它不会改变原来的数组。import numpy as np
np.random.seed(20200614)
x = np.arange(20).reshape((5, 4))
print(x)
# [[ 0 1 2 3]
# [ 4 5 6 7]
# [ 8 9 10 11]
# [12 13 14 15]
# [16 17 18 19]]
y = np.random.permutation(x)
print(y)
# [[ 8 9 10 11]
# [ 0 1 2 3]
# [12 13 14 15]
# [16 17 18 19]
# [ 4 5 6 7]]