On univariate slash distributions, continuous and discrete (Q2183760)

The author investigates general properties of random variables of the form \(Y/U\) (the so-called slash distributions), where \(Y\) and \(U\) are independent random variables with \(Y\) supported on \(\mathbb{R}^+\) and \(U\) uniformly distributed on \((0,1)\), and the more general \(\alpha\)-slash distributions of the form \(Y_\alpha/U^{1/\alpha}\), \(\alpha>0\). Using negative binomial thinning and fattening, discrete analogues of these distributions are also defined and analysed.