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On multiply monotone distributions, continuous or discrete, with applications

  • Claude Lefèvre

    ()

    (ULB - Département de Mathématique [Bruxelles] - Université Libre de Bruxelles)

  • Stéphane Loisel

    ()

    (SAF - Laboratoire de Sciences Actuarielle et Financière - Université Claude Bernard - Lyon I : EA2429)

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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Paper provided by HAL in its series Post-Print with number hal-00750562.

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Date of creation: 2013
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Publication status: Published, Journal of Applied Probability, 2013, 50, 3, 603-907
Handle: RePEc:hal:journl:hal-00750562
Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00750562
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  1. Denuit, Michel & Lefevre, Claude & Mesfioui, M'hamed, 1999. "On s-convex stochastic extrema for arithmetic risks," Insurance: Mathematics and Economics, Elsevier, vol. 25(2), pages 143-155, November.
  2. Denuit, Michel & Lefevre, Claude, 1997. "Some new classes of stochastic order relations among arithmetic random variables, with applications in actuarial sciences," Insurance: Mathematics and Economics, Elsevier, vol. 20(3), pages 197-213, October.
  3. Denuit, Michel & Vylder, Etienne De & Lefevre, Claude, 1999. "Extremal generators and extremal distributions for the continuous s-convex stochastic orderings," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 201-217, May.
  4. Lefèvre, Claude & Loisel, Stéphane, 2010. "Stationary-excess operator and convex stochastic orders," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 64-75, August.
  5. Claude Lefèvre & Stéphane Loisel, 2010. "Stationary-excess operator and convex stochastic orders," Post-Print hal-00442047, HAL.
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