On Uniform and [alpha]-Monotone Discrete Distributions - Jones, M.C (Revstat, 2022)
* 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.