Question

What is the inversion method for simulating a univariate random variable. Why cannot we use this for multivariate continuous random variables ?

Answer 1

The inversion method of sampling involves the follwing steps:

1) Any CDF follows a standard uniform distribution. So draw a sample u from standard uniform U(0,1) distribution.

2) So, now CDF F(x) = u. F(x) is inverted and x is expressed in terms of u. Thus x = F^-1(u). This x is a random sample from the given distribution F.

This method cannot be used for multivariate random variables because the variables may be dependent on each other and hence an explicit equation like (x1,x2,...,xn) = F^-1(u1,u2,...,un) may not be available.

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