On multiply monotone distributions, continuous or discrete, with applications

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.
Complete list of metadatas

Cited literature [27 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00750562
Contributor : Stéphane Loisel <>
Submitted on : Tuesday, November 27, 2012 - 8:56:27 PM
Last modification on : Thursday, February 8, 2018 - 11:09:30 AM
Long-term archiving on : Thursday, February 28, 2013 - 3:46:30 AM

File

AP14365-revision2.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00750562, version 2

Collections

Citation

Claude Lefèvre, Stéphane Loisel. On multiply monotone distributions, continuous or discrete, with applications. Journal of Applied Probability, Applied Probability Trust, 2013, 50 (3), pp.603-907. ⟨hal-00750562v2⟩

Share

Metrics

Record views

318

Files downloads

285