On Uniform and [alpha]-Monotone Discrete Distributions

• Published in: Revstat Vol. 20; no. 4; p. 449
• Main Author: Jones, M.C
• Format: Journal Article
• Language: English
• Published: Instituto Nacional de Estatistica 15.07.2022
• ISSN: 1645-6726
• DOI: 10.57805/revstat.v20i4.381

* In this partly expository article, I am concerned with some simple yet fundamental aspects of discrete distributions that are either uniform or have [alpha]-monotone probability mass functions. In the univariate case, building on work of F.W. Steutel published in 1988, I look at Khintchine's theorem for discrete monotone distributions in terms of mixtures of discrete uniform distributions, along with similar results for discrete [alpha]-monotone distributions. In the multivariate case, I develop a new general family of multivariate discrete distributions with uniform marginal distributions associated with copulas and consider families of multivariate discrete distributions with [alpha]-monotone marginals associated with these. Keywords: * Khintchine's theorem; multivariate geometric distribution; multivariate discrete uniform distribution; multivariate Poisson distribution. AMS Subject Classification: * Primary 62E10, Secondary 62H05.