有没有办法使用Python生成不相关的随机变量? [英] Is there any way to generate uncorrelated random variables using Python?

问题描述

假设我想生成两个随机变量X和Y，它们不相关且均匀分布在[0,1]中.>

生成这样的非常简单的代码如下，它调用了两次 random 函数:

随机导入xT=0yT=0xyT=0对于我在范围内(20000):x = random.random()y = random.random()xT += xyT += yxyT += x*yxyT/20000-xT/20000*yT/20000

然而，随机数实际上是由公式生成的伪随机数，因此它们是相关的.

如何生成两个不相关(或尽可能少相关)的随机变量?

解决方案

关于 RNG 的数学是可靠的.如今，最流行的实现也是如此.因此，您对

的猜想<块引用>

由公式生成，因此它们是相关的.

不正确.

但如果你真的很深刻地这么想，那就有办法了:

Suppose I want to generate two random variables X and Y which are uncorrelated and uniformly distributed in [0,1].

The very naive code to generate such is the following, which calls the random function twice:

import random 
xT=0 
yT=0 
xyT=0 
for i in range(20000):
    x = random.random()
    y = random.random()
    xT += x
    yT += y
    xyT += x*y

xyT/20000-xT/20000*yT/20000

However, the random number is really a pseudo-random number which is generated by a formula, therefore they are correlated.

How to generate two uncorrelated (or correlated as little as possible) random variables?

解决方案

The math on RNGs is solid. These days most popular implementations are too. As such, your conjecture of

is generated by a formula, therefore they are correlated.

is incorrect.

But if you really truly deeply think that way, there is an out: hardware random number generators. The site at random.org has been providing hardware RNG draws "as a service" for a long time. Here is an example (in R, which I use more, but there is an official Python client):

R> library(random)
R> randomNumbers(min=1, max=20000)    # your range, default number
         V1    V2    V3    V4    V5
 [1,]   532 19452  5203 13646  5462
 [2,]  4611 10814  3694 12731   566
 [3,] 11884 19897  1601 10652   791
 [4,] 17427  9524  7522  1051  9432
 [5,]  5426  5079  2232  2517  4883
 [6,] 13807  9194 19980  1706  9205
 [7,] 13043 16250 12827  2161 10789
 [8,]  7060  6008  9110  8388  1102
 [9,] 12042 19342  2001 17780  3100
[10,] 11690  4986  4389 14187 17191
[11,] 19574 13615  3129 17176  5590
[12,] 11104  5361  8000  5260   343
[13,]  7518  7484  7359 16840 12213
[14,] 14914  1991 19952 10127 14981
[15,] 13528 18602 10182  1075 16480
[16,]  9631 17160 19808 11662 10514
[17,]  4827 13960 17003   864 11159
[18,]  8939  7095 16102 19836 15490
[19,]  8321  6007  1787  6113 17948
[20,]  9751  7060  8355 19065 15180
R> 

Edit: The OP seems unconvinced, so there is a quick reproducible simulation (again, in R because that is what I use):

R> set.seed(42)               # set seed for RNG
R> mean(replicate(10, cor(runif(100), runif(100))))
[1] -0.0358398
R> mean(replicate(100, cor(runif(100), runif(100))))
[1] 0.0191165
R> mean(replicate(1000, cor(runif(100), runif(100))))
[1] -0.00117392
R> 

So you see that as we go from 10 to 100 to 1000 replications of just 100 U(0,1), the correlations estimate goes to zero.

We can make this a little nice with a plot, recovering the same data and some more:

R> set.seed(42)
R> x <- 10^(1:5)   # powers of ten from 1 to 5, driving 10^1 to 10^5 sims
R> y <- sapply(x, function(n) mean(replicate(n, cor(runif(100), runif(100)))))
R> y    # same first numbers as seed reset to same start
[1] -0.035839756  0.019116460 -0.001173916 -0.000588006 -0.000290494
R> plot(x, y, type='b', main="Illustration of convergence towards zero", log="x")
R> abline(h=0, col="grey", lty="dotted")

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