On Multiply Monotone Distributions, Continuous or Discrete, with Applications

Abstract

This paper is concerned with the class of distributions, continuous or discrete, whose shape is monotone of finite integer ordert. A characterization is presented as a mixture of a minimum oftindependent uniform distributions. Then, a comparison oft-monotone distributions is made using thes-convex stochastic orders. A link is also pointed out with an alternative approach to monotonicity based on a stationary-excess operator. Finally, the monotonicity property is exploited to reinforce the classical Markov and Lyapunov inequalities. The results are illustrated by several applications to insurance.