多维Erlang混合的次序统计量及其在多生命理论中的应用  

ORDER STATISTICS OF MULTIVARIATE ERLANG MIXTURES WITH APPLICATION IN MULTIPLE LIFETIME THEORY

作　　者：桂文永 张祥雷 杜兴 桑立鑫 GUI Wen-yong;ZHANG Xiang-lei;DU Xing;SANG Li-xin(College of Computer Science and Artificial Intelligence,Wenzhou University,Wenzhou 325000,China;School of Mechanical and Electrical Engineering,Wenzhou University,Wenzhou 325000,China)

机构地区：[1]温州大学计算机与人工智能学院,浙江温州325000 [2]温州大学机电工程学院,浙江温州325000

出　　处：《数学杂志》2022年第3期193-204,共12页Journal of Mathematics

基　　金：Supported by Zhejiang Provincial Natural Science Foundation(LQ17E050003)。

摘　　要：本文研究来自多维Erlang混合分布的具有相关性的随机变量的次序统计量并将相关结论应用到多生命理论中.利用熟知的数学归纳法推导出次序统计量分布密度函数的解析表达式并证明其分布为一维Erlang混合分布,寿险精算理论中常见的重要统计量可以算出精确解.这一结论将随机变量相互独立情形下的结果推广到变量存在相关性的情形.In this paper,we study the order statistics of a set of dependent variables from a multivariate Erlang mixture and then apply the result to multiple lifetime theory.We derive the analytic density functions of the order statistics using the known mathematical induction method and show that any order statistic still has the form of a univariate Erlang mixture.Serval important quantities in life insurance actuarial field also have explicit expressions.The result extends the result of independent random variables to dependent case.

关 键 词：次序统计量 多维Erlang混合 多生命理论 相关性 

分 类 号：O212.1[理学—概率论与数理统计]