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Article Dans Une Revue Journal of Applied Probability Année : 2013

On multiply monotone distributions, continuous or discrete, with applications

Résumé

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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Dates et versions

hal-00750562 , version 1 (10-11-2012)
hal-00750562 , version 2 (27-11-2012)

Identifiants

  • HAL Id : hal-00750562 , version 2

Citer

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