Journal of Applied Probability
- J. Appl. Probab.
- Volume 50, Number 3 (2013), 827-847.
On multiply monotone distributions, continuous or discrete, with applications
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.
J. Appl. Probab., Volume 50, Number 3 (2013), 827-847.
First available in Project Euclid: 5 September 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62E10: Characterization and structure theory 60E15: Inequalities; stochastic orderings
Secondary: 62P05: Applications to actuarial sciences and financial mathematics 60E10: Characteristic functions; other transforms
Lefèvre, Claude; Loisel, Stéphane. On multiply monotone distributions, continuous or discrete, with applications. J. Appl. Probab. 50 (2013), no. 3, 827--847. doi:10.1239/jap/1378401239. https://projecteuclid.org/euclid.jap/1378401239