2 random variables with a Joint Cauchy Distribition
What are the marginal densities? (Integrate out the dependent variable)
What are the modes?
What are the modal dispersions?
The Cauchy distribution is the Student t distribution with one degree
of freedom.
The covariace matrix is:
sig11 sig12
sig12 sig22
sig12 is in both diagonals, because covariance matrix is symmetric
The matlab code for bivariate cauchy is like this:
let cov matrix = z. x = [x1;x2] mu = [mu1,mu2]
f = (gamma(3/2) / (pi()*gamma(1/2)))*det(z)^-1/2*(1+transpose(x-mu)*z^-1*(x-mu))^-3/2