On multiply monotone distributions, continuous or discrete, with applications

Claude Lefèvre (1) , Stéphane Loisel (2)

1 ULB - Département de Mathématique [Bruxelles]
2 SAF - Laboratoire de Sciences Actuarielle et Financière

This paper is concerned with the class of distributions, continuous or discrete, whose shape is monotone of finite integer order t. A characterization is presented as a mixture of a minimum of t independent uniform distributions. Then, a comparison of t-monotone distributions is made using the s-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.

Domaines: Economies et finances; Probabilités [math.PR]

Claude Lefèvre, Stéphane Loisel. On multiply monotone distributions, continuous or discrete, with applications. 2012. ⟨hal-00750562v1⟩