调整随机数列表的平均值和标准差

Question

我必须创建一个介于 -3 和 3 之间的随机数(带小数(列表。问题是列表的平均值必须为 0，标准差必须为 1。如何调整均值和标准差参数？有我可以使用的功能吗？

我已经能够创建一个介于 -3 和 3 之间的随机数列表。

import random

def lista_aleatorios(n):
    lista = [0] * n
    for i in range(n):
        lista[i] = random.uniform(-3, 3)
    return lista
print("nHow many numbers do you want?: ")
n = int(input())
print (lista_aleatorios(n))

Answer 1

函数 random.normalvariate(mu, sigma) 允许您指定正态分布随机变量的平均值和 stdev。

Answer 2

使用 random.gauss ，然后缩放：

import numpy as np
from random import gauss
def bounded_normal(n, mean, std, lower_bound, upper_bound):
    # generate numbers between lower_bound and upper_bound
    result = []
    for i in range(n):
        while True:
            value = gauss(mean, std)
            if lower_bound < value < upper_bound:
                break
        result.append(value)
    # modify the mean and standard deviation
    actual_mean = np.mean(result)
    actual_std = np.std(result)
    mean_difference = mean - actual_mean
    std_difference = std / actual_std
    new_result = [(element + mean_difference) * std_difference for element in result]
    return new_result

Answer 3

好的

，这是快速的解决方案(如果你想使用截断的高斯(。设置边界和所需的标准。我假设平均值为 0。然后快速粗略的代码对分布sigma进行二进制搜索，求解非线性根(brentq()应该在生产代码中使用(。所有公式均取自 Wiki 页面的截断法线。它(sigma(应大于所需的标准dev，因为截断会删除导致较大标准差值的随机值。然后我们做快速抽样测试 - 平均值和 stddev 接近期望值，但永远不会完全等于它们。代码(Python-3.7，Anaconda，Win10 x64(

import numpy as np
from scipy.special import erf
from scipy.stats import truncnorm
def alpha(a, sigma):
    return a/sigma
def beta(b, sigma):
    return b/sigma
def xi(x, sigma):
    return x/sigma
def fi(xi):
    return 1.0/np.sqrt(2.0*np.pi) * np.exp(-0.5*xi*xi)
def Fi(x):
    return 0.5*(1.0 + erf(x/np.sqrt(2.0)))
def Z(al, be):
    return Fi(be) - Fi(al)
def Variance(sigma, a, b):
    al = alpha(a, sigma)
    be = beta(b, sigma)
    ZZ = Z(al, be)
    return sigma*sigma*(1.0 + (al*fi(al) - be*fi(be))/ZZ - ((fi(al)-fi(be))/ZZ)**2)
def stddev(sigma, a, b):
    return np.sqrt(Variance(sigma, a, b))
m = 0.0 # mean
s =  1.0 # this is what we want
a = -3.0 # left boundary
b =  3.0 # right boundary
#print(stddev(s , a, b))
#print(stddev(s + 0.1, a, b))
slo = 1.0
shi = 1.1
stdlo = stddev(slo, a, b)
stdhi = stddev(shi, a, b)
sigma = -1.0
while True: # binary search for sigma
    sme = (slo + shi) / 2.0
    stdme = stddev(sme, a, b)
    if stdme - s == 0.0:
        sigma = stdme
        break
    elif stdme - s < 0.0:
        slo = sme
    else:
        shi = sme
    if shi - slo < 0.0000001:
        sigma = (shi + slo) / 2.0
        break
print(sigma) # we got it, shall be slightly bigger than s, desired stddev
np.random.seed(73123457)
rvs = truncnorm.rvs(a, b, loc=m, scale=sigma, size=1000000) # quick sampling test
print(np.mean(rvs))
print(np.std(rvs))

对我来说，它打印了

sigma = 1.0153870105743408
mean = -0.000400729471992301
stddev = 1.0024267696681475

使用不同的种子或序列长度，您可能会得到这样的输出

1.0153870105743408
-0.00015923177289006116
0.9999974266369461