| Abstract: |
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. |