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identifierxA Study on Bivariate Lifetime Distributions with Multiple Dynamic Competing Risks and Its Applications to Life Insurance2017Y ĬYtTŐYP YDoctor(XDoctoral Thesis 䲑XՌ TXՔ \ tXֽ X xt ٳ tǘ ¤\X
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t @ Ő| L ųD \ X Ĭ̸̐ \ 2016DĳX @ 9D ȩX 1 ǔ X D p\. 0 @ | tǩX xļ th| DPt , X ̸@ l| \.;Under variable complex operating environment, various factors can affect the lifetimes of systems. In this research, we study bivariate reliability models having multiple dynamic competing risks. As competing risks, in addition to the natural failure, we consider the increased stress caused by the failure of one component, external shocks, and the level of stress of the working environment at the same time. Considering two reliability models which take into account all of these competing risks, we derive bivariate life distributions which uses classes of bivariate distribution based on three types of stochestic order. The approach is based on the stochastic modelling of the residual lifetime of an item after the failure of the other item. Furthermore, we compare these two models, and also compare the distributions of maximum and minimum statistics in the two models.
In this paper, we use Modela!, which is more realistic model of the two proposed models, to cover application problems in life insurance. After obtaining bivariate reliability distributions according to two parametric functions (), using four distributions of the residual lifetime (Weibull distribution, Gompertz distribution, Makeham distribution, Polynomial distribution) in the Last-Survivor Status, the simulation of realistic parametric values is performed by applying the average age of men and women in the 2016 Statistics Korea, assuming that a the residual lifetime is independent of men and women. Use simulation results obtained to compare the survival functions of each factor and to calculate the net single premium and the risk of an insurance and an annuity in respect of a last-survivor status.~http://dspace.ewha.ac.kr/handle/2015.oak/236493;
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