Simulating bivariate distribution?

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SUMMARY

This discussion focuses on simulating bivariate distributions using uniformly distributed variables. The process involves finding the marginal distribution of X, drawing a simulated value of X, and then using the joint distribution Fxy(x0, Y) to simulate a value of Y. Lee outlines a clear method to achieve this, emphasizing the importance of the inverse cumulative distribution function in the simulation process.

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zli034
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Hi:

From the undergraduate study we know that if we want to simulate a random variable x with distribution Fx(x). We just make Fx(x)=u, u is a uniform distributed variable, find Fx inverse of U. Then we just need to plugin u the uniform distributed random variable.

How about we have Fxy(x,y). How do we simulate this distribution if we only have uniformly distributed variables to plugin?

Any clues?

Lee
 
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1. Find the marginal distribution of X.

2. Using a 1-dimensional method, draw a simulated value of X based on the marginal distribution-- say it's x0.

3. Fxy(x0, Y) is a 1-dimensional pdf. Use a 1-dimensional method to simulate a value of Y.
 
cool, now I can build simulation to check my homework answers.
 

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