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On Multiply Monotone Distributions, Continuous or Discrete, with Applications

  • Claude Lefèvre (a1) and Stéphane Loisel (a2)

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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Copyright

© Applied Probability Trust 

Corresponding author

∗ Postal address: Département de Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP 210, B-1050 Bruxelles, Belgium. Email address: clefevre@ulb.ac.be
∗∗ Postal address: Université de Lyon, Université Claude Bernard Lyon 1, I.S.F.A., 50 Avenue Tony Garnier, F-69007 Lyon, France. Email address: stephane.loisel@univ-lyon1.fr

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On Multiply Monotone Distributions, Continuous or Discrete, with Applications

  • Claude Lefèvre (a1) and Stéphane Loisel (a2)

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