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Generating correlated random variables via gausssian copula

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  1. Jun 12, 2017 #1
    1. The problem statement, all variables and given/known data

    I want to generate two random variables, one is normally distributed N ~N(10, 25) and the other one, E, is exponentially distributed with mean 1. I was not given a particular correlation coefficient.


    2. Relevant equations
    normal cdf, exponential cdf, inverse transform method.

    3. The attempt at a solution
    First I get two independent standard normals A, B.
    Then I generate a correlated normal C, with unknown correlation coefficient p through a linear combination of A, B, C = pA + sqrt{1-p^2}B. To get N, I simply transform A such as N = 10 + 5A. Then I use the normal CDF to get the unif(0,1) variable corresponding with C, F(C) = U where U~unif(0,1). From inverse transform of exponential cdf, I get that E = -ln(1-U). Is this a correct approach? I am also not sure if given the information in the first two lines I could have inferred some correlation coefficient p.
     
  2. jcsd
  3. Jun 12, 2017 #2

    andrewkirk

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    Yes that approach is correct. It is not possible to infer the correlation coefficient. The Gaussian copula is a one-parameter joint distribution of two uniform RVs, and that parameter is p. In this problem, any value of p in the range [-1,1] can be chosen, although the lecturer might think you were being a smart-alec if you chose 0, 1 or -1.
     
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