This paper is concerned with the class of distributions, continuous ordiscrete, whose shape is monotone of finite integer order t. Acharacterization is presented as a mixture of a minimum of tindependent uniform distributions. Then, a comparison of t-monotonedistributions is made using the s-convex stochastic orders. A link isalso pointed out with an alternative approach to monotonicity based ona stationary-excess operator. Finally, the monotonicity property isexploited to reinforce the classical Markov and Lyapunov inequalities.The results are illustrated by several applications to insurance.
"On multiply monotone distributions, continuous or discrete, with applications." J. Appl. Probab. 50 (3) 827 - 847, September 2013. https://doi.org/10.1239/jap/1378401239