Some equivalent conditions on the classes of lighted-tailed and heavily heavy-tailed and lightly heavy-tailed d.f.s are introduced.The limit behavior of xα(x) and e λx(x) are discussed.Some properties of the subcla...Some equivalent conditions on the classes of lighted-tailed and heavily heavy-tailed and lightly heavy-tailed d.f.s are introduced.The limit behavior of xα(x) and e λx(x) are discussed.Some properties of the subclass DKc and subclass DK 1 are obtained.展开更多
For multivariate failure time with auxiliary covariate information,an estimated pseudo-partial-likelihood estimator under the marginal hazard model with distinguishable baseline hazard has been proposed.However,the as...For multivariate failure time with auxiliary covariate information,an estimated pseudo-partial-likelihood estimator under the marginal hazard model with distinguishable baseline hazard has been proposed.However,the asymptotic properties of the corresponding estimated cumulative hazard function have not been studied.In this paper,based on counting process martingale,we use the continuous mapping theorem and Lenglart inequality and prove the consistency of the estimated cumulative hazard function in estimated pseudo-partial-likelihood approach.展开更多
Under some mild conditions, we derive the asymptotic normality of the Nadaraya-Watson and local linear estimators of the conditional hazard function for left-truncated and dependent data. The estimators were proposed ...Under some mild conditions, we derive the asymptotic normality of the Nadaraya-Watson and local linear estimators of the conditional hazard function for left-truncated and dependent data. The estimators were proposed by Liang and Ould-Sa?d [1]. The results confirm the guess in Liang and Ould-Sa?d [1].展开更多
In this paper, we define the Weibull kernel and use it to nonparametric estimation of the probability density function (pdf) and the hazard rate function for independent and identically distributed (iid) data. The bia...In this paper, we define the Weibull kernel and use it to nonparametric estimation of the probability density function (pdf) and the hazard rate function for independent and identically distributed (iid) data. The bias, variance and the optimal bandwidth of the proposed estimator are investigated. Moreover, the asymptotic normality of the proposed estimator is investigated. The performance of the proposed estimator is tested using simulation study and real data.展开更多
A mature mathematical technique called copula joint function is introduced in this paper, which is commonly used in the financial risk analysis to estimate uncertainty. The joint function is generalized to the n-dimen...A mature mathematical technique called copula joint function is introduced in this paper, which is commonly used in the financial risk analysis to estimate uncertainty. The joint function is generalized to the n-dimensional Frank’s copula. In addition, we adopt two attenuation models proposed by YU and Boore et al, respectively, and construct a two-dimensional copula joint probabilistic function as an example to illustrate the uncertainty treatment at low probability. The results show that copula joint function gives us a better prediction of peak ground motion than that resultant from the simple linear weight technique which is commonly used in the traditional logic-tree treatment of model uncertainties. In light of widespread application in the risk analysis from financial investment to insurance assessment, we believe that the copula-based technique will have a potential application in the seismic hazard analysis.展开更多
In order to evaluate the reliability of long-lifetime products with degradation data, a new proportional hazard degradation model is proposed. By the similarity between time-degradation data and stress-accelerated lif...In order to evaluate the reliability of long-lifetime products with degradation data, a new proportional hazard degradation model is proposed. By the similarity between time-degradation data and stress-accelerated lifetime, and the failure rate function of degradation data which is assumed to be proportional to the time covariate, the reliability assessment based on a proportional hazard degradation model is realized. The least squares method is used to estimate the model＇s parameters. Based on the failure rate of the degradation data and the proportion function of the known time, the failure rate and the reliability function under the given time and the predetermined failure threshold can be extrapolated. A long life GaAs laser is selected as a case study and its reliability is evaluated. The results show that the proposed method can accurately describe the degradation process and it is effective for the reliability assessment of long lifetime products.展开更多
This study has provided a starting point for defining and working with Cox models in respect of multivariate modeling. In medical researches, there may be situations, where several risk factors potentially affect pati...This study has provided a starting point for defining and working with Cox models in respect of multivariate modeling. In medical researches, there may be situations, where several risk factors potentially affect patient prognosis, howbeit, only one or two might predict patient’s predicament. In seeking to find out which of the risk factors contribute the most to the survival times of patients, there was the need for researchers to adjust the covariates to realize their impact on survival times of patients. Aside the multivariate nature of the covariates, some covariates might be categorical while others might be quantitative. Again, there might be cases where researchers need a model that has <span style="font-family:Verdana;">the capability of extending survival analysis methods to assessing simulta</span><span style="font-family:Verdana;">neously the effect of several risk factors on survival times. This study unveiled the Cox model as a robust technique which could accomplish the aforementioned cases.</span><span style="font-family:;" "=""> </span><span style="font-family:;" "=""><span style="font-family:Verdana;">An investigation meant to evaluate the ITN-factor vis-à-vis its </span><span style="font-family:Verdana;">contribution towards death due to Malaria was exemplified with the Cox model. Data were taken from hospitals in Ghana. In doing so, we assessed hospital in-patients who reported cases of malaria (origin state) to time until death or censoring (destination stage) as a result of predictive factors (exposure to the malaria parasites) and some socioeconomic variables. We purposefully used Cox models to quantify the effect of the ITN-factor in the presence of other risk factors to obtain some measures of effect that could describe the rela</span><span style="font-family:Verdana;">tionship between the exposure variable and time until death adjusting for</span><span style="font-family:Verdana;"> other variables. PH assumption holds for all three covariates. Sex of patient was insignificant to deaths due to malaria. Age of patient and user status </span></span><span style="font-family:Verdana;">were</span><span style="font-family:Verdana;"> both significant. The magnitude of the coefficient (0.384) of ITN user status depicts its high contribution to the variation in the dependent variable.</span>展开更多
为提升水上交通安全性,减少碰撞事故,提出基于复杂网络的船舶碰撞危险量化模型。通过构建复杂网络和计算关系强度反映船舶间关系,使用径向分布函数(Radial Distribution Function,RDF)分析船舶密度因素,对船舶周围的交通情况进行讨论;...为提升水上交通安全性,减少碰撞事故,提出基于复杂网络的船舶碰撞危险量化模型。通过构建复杂网络和计算关系强度反映船舶间关系,使用径向分布函数(Radial Distribution Function,RDF)分析船舶密度因素,对船舶周围的交通情况进行讨论;采用网络中心性分析船舶冲突因素;运用基于史蒂文斯幂定律的隶属度函数对密度因素和冲突因素进行整合,改进以船舶对为基础的碰撞危险量化方法。为证明模型准确性,进行实例验证并与基于船舶对叠加计算的方法对比,结果表明本模型具有一定的准确性。通过对实际水域情况的分析,讨论相应的预警机制,可用于水上交通情况的监控和危险预警。展开更多
In this paper, based on random left truncated and right censored data, the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function. wh...In this paper, based on random left truncated and right censored data, the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function. which are valid up to a given order statistic of the observations. A precise bound for the errors is obtained which only depends on the index of the last order statistic to be included.展开更多
Under the condition that the total distribution function is continuous and bounded on （ -∞,∞ ）, we constructed estimations for distribution and hazard functions with local polynomial method, and obtained the rate ...Under the condition that the total distribution function is continuous and bounded on （ -∞,∞ ）, we constructed estimations for distribution and hazard functions with local polynomial method, and obtained the rate of strong convergence of the estimations.展开更多
We introduce a new generalization of the exponentiated power Lindley distribution,called the exponentiated power Lindley power series(EPLPS)distribution.The new distribution arises on a latent complementary risks scen...We introduce a new generalization of the exponentiated power Lindley distribution,called the exponentiated power Lindley power series(EPLPS)distribution.The new distribution arises on a latent complementary risks scenario,in which the lifetime associated with a particular risk is not observable;rather,we observe only the maximum lifetime value among all risks.The distribution exhibits decreasing,increasing,unimodal and bathtub shaped hazard rate functions,depending on its parameters.Several properties of the EPLPS distribution are investigated.Moreover,we discuss maximum likelihood estimation and provide formulas for the elements of the Fisher information matrix.Finally,applications to three real data sets show the flexibility and potentiality of the EPLPS distribution.展开更多
基金Supported by the National Natural Science Foundation of China( 1 0 2 71 0 87)
文摘Some equivalent conditions on the classes of lighted-tailed and heavily heavy-tailed and lightly heavy-tailed d.f.s are introduced.The limit behavior of xα(x) and e λx(x) are discussed.Some properties of the subclass DKc and subclass DK 1 are obtained.
基金Supported by the National Natural Science Foundation of China(10771163)
文摘For multivariate failure time with auxiliary covariate information,an estimated pseudo-partial-likelihood estimator under the marginal hazard model with distinguishable baseline hazard has been proposed.However,the asymptotic properties of the corresponding estimated cumulative hazard function have not been studied.In this paper,based on counting process martingale,we use the continuous mapping theorem and Lenglart inequality and prove the consistency of the estimated cumulative hazard function in estimated pseudo-partial-likelihood approach.
基金supported by National Natural Science Foundation of China(No.11301084)Natural Science Foundation of Fujian Province(No.2014J01010)
文摘Under some mild conditions, we derive the asymptotic normality of the Nadaraya-Watson and local linear estimators of the conditional hazard function for left-truncated and dependent data. The estimators were proposed by Liang and Ould-Sa?d [1]. The results confirm the guess in Liang and Ould-Sa?d [1].
文摘In this paper, we define the Weibull kernel and use it to nonparametric estimation of the probability density function (pdf) and the hazard rate function for independent and identically distributed (iid) data. The bias, variance and the optimal bandwidth of the proposed estimator are investigated. Moreover, the asymptotic normality of the proposed estimator is investigated. The performance of the proposed estimator is tested using simulation study and real data.
基金Project of Institute of Crustal Dynamics, China Earthquake Administration (ZDJ2007-1)One Hundred Individual Program of Chinese Academy of Sciences (99M2009M02) National Natural Science Foundation of China (40574022)
文摘A mature mathematical technique called copula joint function is introduced in this paper, which is commonly used in the financial risk analysis to estimate uncertainty. The joint function is generalized to the n-dimensional Frank’s copula. In addition, we adopt two attenuation models proposed by YU and Boore et al, respectively, and construct a two-dimensional copula joint probabilistic function as an example to illustrate the uncertainty treatment at low probability. The results show that copula joint function gives us a better prediction of peak ground motion than that resultant from the simple linear weight technique which is commonly used in the traditional logic-tree treatment of model uncertainties. In light of widespread application in the risk analysis from financial investment to insurance assessment, we believe that the copula-based technique will have a potential application in the seismic hazard analysis.
基金The National Natural Science Foundation of China (No.50405021)
文摘In order to evaluate the reliability of long-lifetime products with degradation data, a new proportional hazard degradation model is proposed. By the similarity between time-degradation data and stress-accelerated lifetime, and the failure rate function of degradation data which is assumed to be proportional to the time covariate, the reliability assessment based on a proportional hazard degradation model is realized. The least squares method is used to estimate the model＇s parameters. Based on the failure rate of the degradation data and the proportion function of the known time, the failure rate and the reliability function under the given time and the predetermined failure threshold can be extrapolated. A long life GaAs laser is selected as a case study and its reliability is evaluated. The results show that the proposed method can accurately describe the degradation process and it is effective for the reliability assessment of long lifetime products.
文摘This study has provided a starting point for defining and working with Cox models in respect of multivariate modeling. In medical researches, there may be situations, where several risk factors potentially affect patient prognosis, howbeit, only one or two might predict patient’s predicament. In seeking to find out which of the risk factors contribute the most to the survival times of patients, there was the need for researchers to adjust the covariates to realize their impact on survival times of patients. Aside the multivariate nature of the covariates, some covariates might be categorical while others might be quantitative. Again, there might be cases where researchers need a model that has <span style="font-family:Verdana;">the capability of extending survival analysis methods to assessing simulta</span><span style="font-family:Verdana;">neously the effect of several risk factors on survival times. This study unveiled the Cox model as a robust technique which could accomplish the aforementioned cases.</span><span style="font-family:;" "=""> </span><span style="font-family:;" "=""><span style="font-family:Verdana;">An investigation meant to evaluate the ITN-factor vis-à-vis its </span><span style="font-family:Verdana;">contribution towards death due to Malaria was exemplified with the Cox model. Data were taken from hospitals in Ghana. In doing so, we assessed hospital in-patients who reported cases of malaria (origin state) to time until death or censoring (destination stage) as a result of predictive factors (exposure to the malaria parasites) and some socioeconomic variables. We purposefully used Cox models to quantify the effect of the ITN-factor in the presence of other risk factors to obtain some measures of effect that could describe the rela</span><span style="font-family:Verdana;">tionship between the exposure variable and time until death adjusting for</span><span style="font-family:Verdana;"> other variables. PH assumption holds for all three covariates. Sex of patient was insignificant to deaths due to malaria. Age of patient and user status </span></span><span style="font-family:Verdana;">were</span><span style="font-family:Verdana;"> both significant. The magnitude of the coefficient (0.384) of ITN user status depicts its high contribution to the variation in the dependent variable.</span>
文摘为提升水上交通安全性,减少碰撞事故,提出基于复杂网络的船舶碰撞危险量化模型。通过构建复杂网络和计算关系强度反映船舶间关系,使用径向分布函数(Radial Distribution Function,RDF)分析船舶密度因素,对船舶周围的交通情况进行讨论;采用网络中心性分析船舶冲突因素;运用基于史蒂文斯幂定律的隶属度函数对密度因素和冲突因素进行整合,改进以船舶对为基础的碰撞危险量化方法。为证明模型准确性,进行实例验证并与基于船舶对叠加计算的方法对比,结果表明本模型具有一定的准确性。通过对实际水域情况的分析,讨论相应的预警机制,可用于水上交通情况的监控和危险预警。
文摘In this paper, based on random left truncated and right censored data, the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function. which are valid up to a given order statistic of the observations. A precise bound for the errors is obtained which only depends on the index of the last order statistic to be included.
文摘Under the condition that the total distribution function is continuous and bounded on （ -∞,∞ ）, we constructed estimations for distribution and hazard functions with local polynomial method, and obtained the rate of strong convergence of the estimations.
文摘We introduce a new generalization of the exponentiated power Lindley distribution,called the exponentiated power Lindley power series(EPLPS)distribution.The new distribution arises on a latent complementary risks scenario,in which the lifetime associated with a particular risk is not observable;rather,we observe only the maximum lifetime value among all risks.The distribution exhibits decreasing,increasing,unimodal and bathtub shaped hazard rate functions,depending on its parameters.Several properties of the EPLPS distribution are investigated.Moreover,we discuss maximum likelihood estimation and provide formulas for the elements of the Fisher information matrix.Finally,applications to three real data sets show the flexibility and potentiality of the EPLPS distribution.
