par Lefèvre, Claude 
;Loisel, Stéphane
Référence Journal of Applied Probability, 50, 3, page (827-847)
Publication Publié, 2013-09
;Loisel, StéphaneRéférence Journal of Applied Probability, 50, 3, page (827-847)
Publication Publié, 2013-09
Article révisé par les pairs
| Résumé : | 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 amixture 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. © Applied Probability Trust 2013. |
