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I have a univariate distribution of the form

[itex]\frac{xγ}{((x^2+γ^2)^{1.5})}[/itex]

where both parameters are real and non-negative.

How do I go about finding the bivariate form, where x and y (the new bivariate variables) are still both real and positive?

To explain further what I mean, the univariate cauchy distribution can be similarily is defined as

[itex]\frac{(γ/∏)}{(x^2+γ^2)}[/itex]

where x and y (in this case) are real numbers which can be positive and negative.

it's bivariate distribution can be defined as

[itex]\frac{(γ/(2∏))}{(x^2+y^2+γ^2)^{1.5}}[/itex]

How was this calculation done? One guess I had was to transform the first equation above into the Fourier domain and therefore obtain it's characteristic function. Transform this somehow in the CF domain and invert. Hmmmm. I seem to be a long way off this at the moment.

Any help would be gratefully received. I have spent at least three weeks mucking around with Matlab, Maple and Mathematica, but not to too much avail.

Thanks in advance

Paul

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# Trying to generate a bivariate distribution from a univariate distribution

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