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Math Help - Joint Cauchy Distribution Problem

  1. #1
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    Joint Cauchy Distribution Problem

    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?
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  2. #2
    MHF Contributor matheagle's Avatar
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    PLEASE write down this joint density.
    I know of the univariate Cauchy, BUT I have no idea what this
    bivariate Cauchy looks like.
    I need to know the correlation between the rvs.
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  3. #3
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    multivariate cauchy

    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
    Last edited by yee lee; October 23rd 2009 at 06:05 AM.
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  4. #4
    MHF Contributor matheagle's Avatar
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    You may think this was helpful, but since I do not know matlab, it isn't.
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