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!