Generating correlated random variables via gausssian copula

In summary, the conversation discusses the process of generating two random variables, one normally distributed and the other exponentially distributed, without a given correlation coefficient. The approach involves obtaining two independent standard normal variables and using a linear combination to generate a correlated normal variable. The normal CDF and inverse transform method are then used to obtain the desired variables. It is not possible to infer the correlation coefficient based on the given information.
  • #1
fignewtons
28
0

Homework Statement



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.

Homework Equations


normal cdf, exponential cdf, inverse transform method.

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.
 
Physics news on Phys.org
  • #2
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.
 

1. What is a Gaussian copula?

A Gaussian copula is a mathematical tool used to generate correlated random variables from a set of independent variables. It is based on the concept of joint probability distribution and allows for the modeling of complex dependencies between random variables.

2. Why is generating correlated random variables important?

Generating correlated random variables is important in many fields, including finance, economics, and climate science. It allows for the modeling of complex relationships between variables and can improve the accuracy of statistical analyses and predictions.

3. How does a Gaussian copula work?

A Gaussian copula works by transforming a set of independent random variables into a multivariate normal distribution. This distribution can then be used to generate correlated random variables by specifying the desired correlation structure.

4. What are the assumptions of a Gaussian copula?

The main assumption of a Gaussian copula is that the underlying variables follow a normal distribution. Additionally, it assumes that the variables have a linear relationship and that the correlation between variables is constant.

5. Are there any limitations to using a Gaussian copula?

While a Gaussian copula is a useful tool for generating correlated random variables, it does have some limitations. It assumes a linear relationship between variables and may not accurately model non-linear dependencies. It also does not account for extreme events or tail dependencies, which may be important in some applications.

Similar threads

  • Calculus and Beyond Homework Help
Replies
7
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
30
Views
2K
  • Calculus and Beyond Homework Help
Replies
9
Views
2K
Replies
12
Views
672
  • Calculus and Beyond Homework Help
Replies
3
Views
957
  • Calculus and Beyond Homework Help
Replies
5
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
690
  • Set Theory, Logic, Probability, Statistics
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
18
Views
1K
  • Calculus and Beyond Homework Help
Replies
6
Views
2K
Back
Top