Hi all(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Trying to generate a bivariate distribution from a univariate distribution

Loading...

Similar Threads for Trying generate bivariate | Date |
---|---|

B Given a success rate of 1% and 100 tries.... | Mar 27, 2018 |

I Probability of an event in n tries | Sep 19, 2017 |

Tri-quadratic equation setup? | Jun 19, 2014 |

Trying to understand an expression in Peano's Principia Arithmetices | Dec 8, 2013 |

**Physics Forums - The Fusion of Science and Community**