On Univariate Slash Distributions, Continuous and Discrete

In this article, I explore in a unified manner the structure of uniform slash and α-slash distributions which, in the continuous case, are defined to be the distributions of Y/U and Yα/U1/α where Y and Yα follow any distribution on ℝ+ and, independently, U is uniform on (0, 1). The parallels with the monotone and α-monotone distributions of Y × U and Yα × U1/α, respectively, are striking. I also introduce discrete uniform slash and α-slash distributions which arise from a notion of negative binomial thinning/fattening. Their specification, although apparently rather different from the continuous case, seems to be a good one because of the close way in which their properties mimic those of the continuous case