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September 2013 On multiply monotone distributions, continuous or discrete, with applications
Claude Lefèvre, Stéphane Loisel
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J. Appl. Probab. 50(3): 827-847 (September 2013). DOI: 10.1239/jap/1378401239

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.

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Claude Lefèvre. Stéphane Loisel. "On multiply monotone distributions, continuous or discrete, with applications." J. Appl. Probab. 50 (3) 827 - 847, September 2013. https://doi.org/10.1239/jap/1378401239

Information

Published: September 2013
First available in Project Euclid: 5 September 2013

zbMATH: 1293.62028
MathSciNet: MR3102517
Digital Object Identifier: 10.1239/jap/1378401239

Subjects:
Primary: 60E15, 62E10
Secondary: 60E10, 62P05

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 3 • September 2013
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