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| 多维Erlang混合的次序统计量及其在多生命理论中的应用 |
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桂文永,张祥雷,杜兴,桑立鑫
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| 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. |
| 关键词: 次序统计量 多维Erlang混合 多生命理论 相关性 |
| DOI： |
| 分类号:O212.1 |
| 基金项目:Supported by Zhejiang Provincial Natural Science Foundation (LQ17E050003). |
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| ORDER STATISTICS OF MULTIVARIATE ERLANG MIXTURES WITH APPLICATION IN MULTIPLE LIFETIME THEORY |
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GUI Wen-yong,ZHANG Xiang-lei,DU Xing,SANG Li-xin
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| Abstract: |
| 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. |
| Key words: order statistics multivariate Erlang mixture multiple life theory dependency |
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