On multiply monotone distributions, continuous or discrete, with applications.

• Autores: Claude Lefèvre, Stéphane Loisel
• Localización: Journal of Applied Probability, ISSN-e 0021-9002, Vol. 50, Nº. 3, 2013, págs. 827-847
• Idioma: inglés
• DOI: 10.1017/s0021900200009876
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• Resumen

  • 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.