On the self-decomposability of the half-Cauchy distribution
The half-Cauchy distribution function \(F(x)\) is determined as follows: \(F(x)=0\) for \(x<0\) and \(F'(x)=2[\pi(1+x^2)]^{-1}\) for \(x\geq 0\). It is shown that this distribution is self-decomposable, that is for any \(0<c<1\) there exists a distribution function \(G_c(x)\) such that \(F(x)\) is equal to the convolution of \(F(x/c)\) and \(G_c(x)\).
self-decomposability of half-Cauchy distribution
scientific article; zbMATH DE number 1215708