Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A Cauchy convolution with other distribution

  1. Jul 18, 2016 #1

    DrDu

    User Avatar
    Science Advisor

    I have a set of data which are probably convolutions of a Cauchy distribution with some other distribution. I am looking for some model for this other distribution so that a tractable analytic formula results. I know that the convolution Cauchy with Cauchy is again Cauchy, but I want the other function in the convolution to have defined first and second moment. Apparently there is a convolution of Cauchy with a normal distribution called Voigt distribution, but there is no analytical formula available. Any ideas?

    Thank you very much!
     
  2. jcsd
  3. Jul 18, 2016 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    I'm rather curious how you know it's a convolution with a Cauchy distribution.
    Do you have any information about this Cauchy distribution? Is it the standard Cauchy distribution? Do you know its median?
     
  4. Jul 18, 2016 #3

    DrDu

    User Avatar
    Science Advisor

    The Cauchy function is a theoretical model for concentration as a function of other concentrations and an equilibrium constant, not a statistical distribution. However I want to fit a distribution of the medians of the equilibrium constant.
     
  5. Jul 19, 2016 #4

    Stephen Tashi

    User Avatar
    Science Advisor

    For what are we seeking an analytical formula - for the probability density function of the convolution ?

    Does that amount to saying:

    Find a non-negative function [itex] g(x) [/itex] such that [itex] \int_{-\infty}^{\infty} g(x) dx [/itex] exists and [itex] \int_{-\infty}^{\infty} \frac{1}{Ax^2 + Bx + C} g(y-x) dx [/itex] has a closed form solution.
     
  6. Jul 19, 2016 #5

    DrDu

    User Avatar
    Science Advisor

    Yes, this was my problem. I solved it using a Sips distribution as g, which is a function of ln x rather than x, and a partial fraction decomposition.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Cauchy convolution with other distribution
Loading...