Journal of Applied Probability

On multiply monotone distributions, continuous or discrete, with applications

Claude Lefèvre and Stéphane Loisel

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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.

Article information

J. Appl. Probab., Volume 50, Number 3 (2013), 827-847.

First available in Project Euclid: 5 September 2013

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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

t-monotone function s-convex stochastic order stationary-excess operator Markov and Lyapunov inequalities insurance risk theory


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.

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