# exponentially correlated random variables

1. ## exponentially correlated random variables

Hi!

I'm currently using this function that works well to generate linearly correlated random variables:

If Z1 and Z2 are each independent standard normal random variables,
i.e., each is NORMINV(RAND(),0,1), then to get X and Y with correlation
rho, use

X = MeanX + StDevX*Z1

Y = MeanY + StDevY*(Z1*rho + Z2*(1-rho^2)^0.5)

Rho is any value from -1 to +1 (-ve to +ve correlation).

This is what the above looks like on a scatter plot:
image1.png

What I need to simulate is something that has this kind of exponential component to it:
image2.png

Thanks
-Lisa

2. ## Re: exponentially correlated random variables

Not sure what it is doing, but to set up randomize value from -1 to 1

rho:
=RAND()*2-1

3. ## Re: exponentially correlated random variables

Can you provide a more worked example? What does "exponentially correlated" mean in your case?

When I think of an exponential correlation, I think of y=b*exp(mx) which translates into log(y)=log(b)+mx when you take the logarithm of both sides. It should be evident that log(y) is a straight line function of x. By taking the logarithm of your y values, you can then use the same techniques you are using for your linear correlation. Is that the kind of problem you are trying to work out, or are you doing something different?

4. ## Re: exponentially correlated random variables

Thanks MrShorty for the idea of applying the log to the Y values, I'll play with that and see if it does the trick.

Hope the images that I attached made it through as they show the 2 cases of correlated values, one linear correlation and the second exponentially correlated. The latter means in my case that as the x-values increase, the y-values will increase (simple correlation), but as X grows, Y should grow faster and faster. This is for research involving pressure (x-axis) and heat generated under volatile conditions (y -axis), thus the need to randomize (or de-correlate) the y-values, but within defined parameters (Rho, but you can call it whatever) in excel function-wise it's =pearson(x,y) except in this case the result of this function is used as one of the inputs to generate Y such that when =pearson(x,y) is run on the generated random correlated variables, it will yield a number close to the correlation coefficient that was requested.

5. ## Re: exponentially correlated random variables

Maybe formulas like the following would produce the type graph you want:
X values: =ROUNDUP(ROWS(A\$1:A1)/5,0)
Y values: =RANDBETWEEN(SUM(A2,-A2/5),PRODUCT(A2,2))
Note that the values will change when the F9 key is pressed.
Let us know if you have any questions.

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