On univariate slash distributions, continuous and discrete

摘要

In this article, I explore in a unified manner the structure of uniform slash and alpha-slash distributions which, in the continuous case, are defined to be the distributions of Y / U and Y alpha/U1/alpha where Y and Y alpha follow any distribution on R+ and, independently, U is uniform on (0, 1). The parallels with the monotone and alpha-monotone distributions of YxU and Y alpha xU1/alpha, respectively, are striking. I also introduce discrete uniform slash and alpha-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.