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离散的5阶凸随机序的极值分布及其应用 被引量：1

Extremal distribution for the discrete 5-convex stochastic ordering and applications
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摘要 获得了离散的5阶凸随机序的极值分布。作为应用,研究了分支过程中最终灭绝概率以及经典离散风险模型中Lunberg调整系数的上下界估计。 The extremal distribution for the discrete 5-convex order was obtained. In applications, the lower and upper bounds for the probability of extinction in a branching process and the Lundberg＇s adjustment coefficient in the classical discrete risk model were studied.
作者 田有功 焦桂梅
机构地区 兰州商学院信息工程学院 兰州大学数学与统计学院
出处 《山东大学学报（理学版）》 CAS CSCD 北大核心 2014年第1期99-104,共6页 Journal of Shandong University(Natural Science)
基金 国家自然科学基金资助项目(41271038)
关键词 5阶凸随机序 矩空间 极值分布 分支过程 Lunberg调整系数 5-convex order moment space extremal distribution branching process Lundberg＇s adjustment coeffi-cient
分类号 O211.6 [理学—概率论与数理统计]
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参考文献13

  • 1KAAS R,VAN HEERWAARDEN A E,GOOVAERTS M J. Ordering of actuarial risks[M].Brussels:CAIRE,1994.
  • 2DENUIT M,DHAENE J,GOOVAERTS M. Actuarial theory for dependent risks:measures,ordersand models[M].New York:Wiley Press,2006.
  • 3SHAKED M,SHANTHIKUMAR J G. Stochastic orders and their applications[M].{H}New York:Springer-Verlag,2006.
  • 4FISHBURN P C,LAVALLE I H. Stochastic dominance on unidimensional grid[J].{H}Mathematics of Operations Research,1995,(03):513-525.
  • 5LEFèVRE C,UTEV S. Comparing sums of exchangeable Bernoulli random variables[J].{H}Journal of Applied Probability,1996,(02):285-310.
  • 6DENUIT M,DE VYLDER E,LEFèVRE C. Extremal generators and extremal distributions for the continuous s-convex sto-chastic orderings[J].{H}Insurance:Mathematics and Economics,1999,(03):201-217.
  • 7DENUIT M,LEFèVRE C. Some new classes of stochastic order relations among arithmetic random variables with applications in actuarial sciences[J].{H}Insurance:Mathematics and Economics,1997,(03):197-214.
  • 8DENUIT M,LEFèVRE C,MESFIOUI M. On s-convex stochastic extrema for arithmetic risks[J].{H}Insurance:Mathematics and Economics,1999,(02):143-155.
  • 9COURTOIS C,DENUIT M,BELLEGEM S V. Discrete s-convex extremal distributions:theory and applications[J].Applied Mathematics Letters,2006,(12):1367-1377.
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同被引文献13

  • 1KAAS R,VAN HEERWAARDEN A E,GOOVAERTS M.Ordering of actuarial risks[M].Brussels:CAIRE,1994.
  • 2SHAKED M,S J G.Stochastic orders and their applications[ M].New York:Springer,2006.
  • 3DENUIT M,DHAENE J,GOOVAERTS M,et al.Actuarial theory for dependent risks:measures,orders and models[ M ].New York:Wiley,2005.
  • 4FISHBURN P C,LAVALLE I H.Stochastic dominance on unidimensional grids[ J].Mathematics of Operations Research,1995,20(3):513-525.
  • 5DENUIT M,LEFEVRE C L.Some new classes of stochastic order relations among arithmetic random variables with applica-tions in actuarial sciences [ J ].Insurance:Mathematics and Economics,1997,20(3):197-214.
  • 6DENUIT M,LEFEVRE C L,MESFIOUI M.On s-convex stochastic extrema for arithmetic risks[ J].Insurance:Mathematics and Economics,1999,25(2):143-155.
  • 7COURTOIS C,DENUIT M,BELLEGEM S V.Discrete s-convex extremal distributions:Theory and applications [ J ].Applied Mathematics Letters,2006,19(12):1367-1377.
  • 8DENU1T M,LEFEVRE C L,UTEV S.Stochastic orderings of convex/concave type on an arbitrary grid[ J ].Mathematics of Operations Research,1999,24(4):835-846.
  • 9COURTOIS C,DENUIT M.S-convex extremal distributions with arbitrary discrete support[ J].Journal of Mathematical Ine-qualities,2008,2(2):197-214.
  • 10DENUIT M,LEFEVRE C L,SHAKED M.The s-convex orders among real random variables with applications [ J ].Mathe-matical Inequalities and Applications,1998,1(4):585-613.

引证文献1

山东大学学报（理学版）
2014年 第1期

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