How to generate random numbers correlated to a given dataset in Python

Question

I have a 20 element array, x, of floating point numbers, ex:

x = [ 0.35945087, 0.08999019, 0.51313128, 0.75455967, 0.50654956, 0.12404178, 0.25115332, 0.94167661, 0.95727792, 0.35572299, 0.65264679, 0.09416763, 0.861585, 0.19661212, 0.62882119, 0.1180147, 0.17153433, 0.07275386, 0.01895795, 0.00578392]

This data is not normally distributed, it rather follows a power law distribution.

I need to generate a second array, y, which is correlated with x and the correlation coefficient is 0.70.

How do I do this with python?

Possibly duplicate with Generating random correlated x and y points using Numpy — SparkAndShine
– SparkAndShine, Commented May 9, 2016 at 14:38
This is not a duplicate of that question. This is a more complicated problem because of the constraint on the marginal distribution. — Robert Kern
– Robert Kern, Commented May 9, 2016 at 15:00

Robert Kern · Accepted Answer · 2016-05-09 15:53:19Z

1

This is one of those things that sounds very easy to ask, but is complicated when you get down to the details. I can only point you in the right direction rather than give you a straightforward recipe.

Notionally, what you need to do is construct a bivariate distribution where the marginal distributions are both power laws (presumably, the same power law) but has the desired correlation coefficient.

(X, Y) ~ f(x, y) s.t. X ~ powerlaw(params); Y ~ powerlaw(params); corr(X, Y) = 0.7

This can be done through a copula.

For each sample x[i] that you have, you find the univariate conditional distribution Y ~ f(x=x[i], y) and sample from it.

Note that the correlation coefficient is probably not particularly meaningful when applied to power law distributions. Power law distributions do not in general have finite first and second moments.

answered May 9, 2016 at 15:53

Robert Kern

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Comments

SwissFr · Accepted Answer · 2016-05-09 14:48:57Z

-3

y = [number * 0.7 for number in x]

Is this what you need ?

edited May 9, 2016 at 14:48

answered May 9, 2016 at 14:34

SwissFr

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3 Comments

Paba Over a year ago

unfortunately this won't work. According to your approach the correlation between x and y remains 1.

Robert Kern Over a year ago

The correlation coefficient is still 1.

gariepy Over a year ago

Thanks for your submission to StackOverflow! In general, it is highly recommended to post your solution with some explanation rather than ask for feedback from the original poster (OP).

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