On Multiply Monotone Distributions, Continuous or Discrete, with Applications
نویسندگان
چکیده
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. MSC: primary 62E10, 60E15; secondary 62P05, 60E10
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عنوان ژورنال:
- J. Applied Probability
دوره 50 شماره
صفحات -
تاریخ انتشار 2013