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.
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Journal of Applied Probability, Applied Probability Trust, 2013, 50 (3), pp.603-907
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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〉

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