On Uniform and α-Monotone Discrete Distributions


  • M.C. Jones The Open University




Khintchine’s theorem, multivariate geometric distribution, multivariate discrete uniform distribution, multivariate Poisson distribution


In this partly expository article, I am concerned with some simple yet fundamental aspects of discrete distributions that are either uniform or have α-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 α-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 α-monotone marginals associated with these.



How to Cite

Jones , M. (2022). On Uniform and α-Monotone Discrete Distributions. REVSTAT-Statistical Journal, 20(4), 449–462. https://doi.org/10.57805/revstat.v20i4.381