The stationary Gamma-OU processes are recommended to be the volatility of the financial assets.A parametric estimation for the Gamma-OU processes based on the discrete observations is considered in this paper.The esti...The stationary Gamma-OU processes are recommended to be the volatility of the financial assets.A parametric estimation for the Gamma-OU processes based on the discrete observations is considered in this paper.The estimator of an intensity parameter A and its convergence result are given,and the simulations show that the estimation is quite accurate.Assuming that the parameter A is estimated,the maximum likelihood estimation of shape parameter c and scale parameter a,whose likelihood function is not explicitly computable,is considered.By means of the Gaver-Stehfest algorithm,we construct an explicit sequence of approximations to the likelihood function and show that it converges the true(but unkown)one.Maximizing the sequence results in an estimator that converges to the true maximum likelihood estimator and the approximation shares the asymptotic properties of the true maximum likelihood estimator.Some simulation experiments reveal that this method is still quite accurate in most of rational situations for the background of volatility.展开更多
【目的】工程技术领域中的系统退化受用户操作、制造工艺、工作环境等多种因素影响,系统初始状态和退化速率之间通常存在相关性(Correlation between the Initial State and the Degradation Rate, CISDR)和动态协变量在退化模型中是需...【目的】工程技术领域中的系统退化受用户操作、制造工艺、工作环境等多种因素影响,系统初始状态和退化速率之间通常存在相关性(Correlation between the Initial State and the Degradation Rate, CISDR)和动态协变量在退化模型中是需要考虑的关键因素,但同时考虑以上两类随机性的文献鲜见。针对上述问题,基于Gamma退化过程建立了考虑动态协变量及系统初始退化状态与退化率相关的可靠性模型来进行研究、分析。【方法】首先,建立剩余寿命预测模型,基于对系统运行过程中的状态监测数据的统计分析,推断出产品的剩余寿命分布;其次,针对系统退化周期内操作、运行环境的差异,使用奥恩斯坦-乌伦贝克(Ornstein-Uhlenbeck, OU)过程刻画了动态协变量变化,建立了考虑动态协变量的Gamma退化模型;再次,通过指数效应模型建立动态协变量与退化率之间的关联;最后,使用二元正态分布建立系统初始退化状态与退化率相关性模型,推导得到了系统可靠度函数与剩余寿命的概率密度。【结果】结果表明,仿真算例和应用实例验证了所建立的模型能够显著提高剩余寿命预测的准确性,同时考虑两种随机效应后的剩余寿命预测更加客观。展开更多
基金This work was supported by National Natural Science Foundation of China(Grant No.10371074).
文摘The stationary Gamma-OU processes are recommended to be the volatility of the financial assets.A parametric estimation for the Gamma-OU processes based on the discrete observations is considered in this paper.The estimator of an intensity parameter A and its convergence result are given,and the simulations show that the estimation is quite accurate.Assuming that the parameter A is estimated,the maximum likelihood estimation of shape parameter c and scale parameter a,whose likelihood function is not explicitly computable,is considered.By means of the Gaver-Stehfest algorithm,we construct an explicit sequence of approximations to the likelihood function and show that it converges the true(but unkown)one.Maximizing the sequence results in an estimator that converges to the true maximum likelihood estimator and the approximation shares the asymptotic properties of the true maximum likelihood estimator.Some simulation experiments reveal that this method is still quite accurate in most of rational situations for the background of volatility.
文摘【目的】工程技术领域中的系统退化受用户操作、制造工艺、工作环境等多种因素影响,系统初始状态和退化速率之间通常存在相关性(Correlation between the Initial State and the Degradation Rate, CISDR)和动态协变量在退化模型中是需要考虑的关键因素,但同时考虑以上两类随机性的文献鲜见。针对上述问题,基于Gamma退化过程建立了考虑动态协变量及系统初始退化状态与退化率相关的可靠性模型来进行研究、分析。【方法】首先,建立剩余寿命预测模型,基于对系统运行过程中的状态监测数据的统计分析,推断出产品的剩余寿命分布;其次,针对系统退化周期内操作、运行环境的差异,使用奥恩斯坦-乌伦贝克(Ornstein-Uhlenbeck, OU)过程刻画了动态协变量变化,建立了考虑动态协变量的Gamma退化模型;再次,通过指数效应模型建立动态协变量与退化率之间的关联;最后,使用二元正态分布建立系统初始退化状态与退化率相关性模型,推导得到了系统可靠度函数与剩余寿命的概率密度。【结果】结果表明,仿真算例和应用实例验证了所建立的模型能够显著提高剩余寿命预测的准确性,同时考虑两种随机效应后的剩余寿命预测更加客观。
