On univariate slash distributions, continuous and discrete

M. C. Jones ()
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M. C. Jones: The Open University

Annals of the Institute of Statistical Mathematics, 2020, vol. 72, issue 3, No 1, 645-657

Abstract: Abstract In this article, I explore in a unified manner the structure of uniform slash and $$\alpha $$α-slash distributions which, in the continuous case, are defined to be the distributions of Y / U and $$ Y_\alpha /U^{1/\alpha }$$Yα/U1/α where Y and $$Y_\alpha $$Yα follow any distribution on $$\mathbb {R}^+$$R+ and, independently, U is uniform on (0, 1). The parallels with the monotone and $$\alpha $$α-monotone distributions of $$ Y \times U$$Y×U and $$Y_\alpha \times U^{1/\alpha }$$Yα×U1/α, respectively, are striking. I also introduce discrete uniform slash and $$\alpha $$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.

Keywords: Binomial thinning; Monotone density; Negative binomial fattening; Uniform random variable (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10463-019-00708-4

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