The paper discusses the statistical inference problem of the compound Poisson vector process(CPVP)in the domain of attraction of normal law but with infinite covariance matrix.The empirical likelihood(EL)method to con...The paper discusses the statistical inference problem of the compound Poisson vector process(CPVP)in the domain of attraction of normal law but with infinite covariance matrix.The empirical likelihood(EL)method to construct confidence regions for the mean vector has been proposed.It is a generalization from the finite second-order moments to the infinite second-order moments in the domain of attraction of normal law.The log-empirical likelihood ratio statistic for the average number of the CPVP converges to F distribution in distribution when the population is in the domain of attraction of normal law but has infinite covariance matrix.Some simulation results are proposed to illustrate the method of the paper.展开更多
Existing structures may suffer from resistance deterioration due to repeated attacks. The modeling of resistance deterioration is a critical ingredient in the reliability assessment and service life prediction of thes...Existing structures may suffer from resistance deterioration due to repeated attacks. The modeling of resistance deterioration is a critical ingredient in the reliability assessment and service life prediction of these degraded structures. In this paper, an explicit compound Poisson process-based model is developed to describe the shock deterioration of structural resistance, where the magnitude of each shock deterioration increment is modeled by a Gamma-distributed random variable. The moments(mean value and variance) and the distribution function of the cumulative shock deterioration are derived in a closed form, based on a proposed W-function. A method for the efficient calculation of the W-function is presented,which reduces to the Bessel type I function if the shock deterioration increment is exponentially distributed(a special case of Gamma distribution). The proposed shock deterioration model is applicable to either a stationary or a nonstationary Poisson process of random jumps.Subsequently, the overall resistance deterioration is modeled as the linear combination of gradual and shock deteriorations, based on which the proposed model can be used in the timedependent reliability assessment of aging structures efficiently. A numerical example is presented to demonstrate the applicability of the proposed deterioration model by estimating the time-dependent reliability of an aging bridge. It is found that a smaller threshold for the degraded resistance leads to greater mean value and standard deviation of the time to failure,and this effect is enhanced by a smaller occurrence rate of the shock deterioration.展开更多
By the Cramér method, the large deviation principle for a form of compound Poisson process S(t)=∑N(t)i=1h(t-Si)Xi is obtained,where N(t), t>0, is a nonhomogeneous Poisson process with intensity λ(t)>0, Xi...By the Cramér method, the large deviation principle for a form of compound Poisson process S(t)=∑N(t)i=1h(t-Si)Xi is obtained,where N(t), t>0, is a nonhomogeneous Poisson process with intensity λ(t)>0, Xi, i≥1, are i.i.d. nonnegative random variables independent of N(t), and h(t), t>0, is a nonnegative monotone real function. Consequently, weak convergence for S(t) is also obtained.展开更多
In the present paper surplus process perturbed by diffusion are considered. The distributions of the surplus immediately before and at ruin corresponding to the probabilities of ruin caused by oscillation and ruin cau...In the present paper surplus process perturbed by diffusion are considered. The distributions of the surplus immediately before and at ruin corresponding to the probabilities of ruin caused by oscillation and ruin caused by a claim are studied. Some joint distribution densities are obtained. Techniques from martingale theory and renewal theory are used.展开更多
Although Geometric Brownian Motion and Jump Diffusion Models have largely dominated the literature on asset price modeling, studies of the empirical stock price data on the Ghana Stock Exchange have led to the conclus...Although Geometric Brownian Motion and Jump Diffusion Models have largely dominated the literature on asset price modeling, studies of the empirical stock price data on the Ghana Stock Exchange have led to the conclusion that there are some stocks in which the return processes consistently depart from these models in theory as well as in its statistical properties. This paper gives a fundamental review of the development of a stock price model based on pure jump processes to capture the unique behavior exhibited by some stocks on the Exchange. Although pure jump processes have been examined thoroughly by other authors, there is a lack of mathematical clarity in terms of deriving the underlying stock price process. This paper provides a link between stock prices existing on a measure space to its development as a pure jump Levy process. We test the suitability of the model to the empirical evidence using numerical procedures. The simulation results show that the trajectories of the model are a better fit for the empirical data than those produced by the diffusion and jump diffusion models.展开更多
基金Characteristic Innovation Projects of Ordinary Universities of Guangdong Province,China(No.2022KTSCX150)Zhaoqing Education Development Institute Project,China(No.ZQJYY2021144)Zhaoqing College Quality Project and Teaching Reform Project,China(Nos.zlgc202003 and zlgc202112)。
文摘The paper discusses the statistical inference problem of the compound Poisson vector process(CPVP)in the domain of attraction of normal law but with infinite covariance matrix.The empirical likelihood(EL)method to construct confidence regions for the mean vector has been proposed.It is a generalization from the finite second-order moments to the infinite second-order moments in the domain of attraction of normal law.The log-empirical likelihood ratio statistic for the average number of the CPVP converges to F distribution in distribution when the population is in the domain of attraction of normal law but has infinite covariance matrix.Some simulation results are proposed to illustrate the method of the paper.
基金supported by the Vice-Chancellor’s Postdoctoral Research Fellowship from the University of Wollongong。
文摘Existing structures may suffer from resistance deterioration due to repeated attacks. The modeling of resistance deterioration is a critical ingredient in the reliability assessment and service life prediction of these degraded structures. In this paper, an explicit compound Poisson process-based model is developed to describe the shock deterioration of structural resistance, where the magnitude of each shock deterioration increment is modeled by a Gamma-distributed random variable. The moments(mean value and variance) and the distribution function of the cumulative shock deterioration are derived in a closed form, based on a proposed W-function. A method for the efficient calculation of the W-function is presented,which reduces to the Bessel type I function if the shock deterioration increment is exponentially distributed(a special case of Gamma distribution). The proposed shock deterioration model is applicable to either a stationary or a nonstationary Poisson process of random jumps.Subsequently, the overall resistance deterioration is modeled as the linear combination of gradual and shock deteriorations, based on which the proposed model can be used in the timedependent reliability assessment of aging structures efficiently. A numerical example is presented to demonstrate the applicability of the proposed deterioration model by estimating the time-dependent reliability of an aging bridge. It is found that a smaller threshold for the degraded resistance leads to greater mean value and standard deviation of the time to failure,and this effect is enhanced by a smaller occurrence rate of the shock deterioration.
基金National Natural Science Foundation of China(No. 10971157)Educational Commission of Hubei Province, China(No.2004X124)
文摘By the Cramér method, the large deviation principle for a form of compound Poisson process S(t)=∑N(t)i=1h(t-Si)Xi is obtained,where N(t), t>0, is a nonhomogeneous Poisson process with intensity λ(t)>0, Xi, i≥1, are i.i.d. nonnegative random variables independent of N(t), and h(t), t>0, is a nonnegative monotone real function. Consequently, weak convergence for S(t) is also obtained.
基金Supported by the National Natural Sciences Foundation of China (No.19971047).
文摘In the present paper surplus process perturbed by diffusion are considered. The distributions of the surplus immediately before and at ruin corresponding to the probabilities of ruin caused by oscillation and ruin caused by a claim are studied. Some joint distribution densities are obtained. Techniques from martingale theory and renewal theory are used.
文摘Although Geometric Brownian Motion and Jump Diffusion Models have largely dominated the literature on asset price modeling, studies of the empirical stock price data on the Ghana Stock Exchange have led to the conclusion that there are some stocks in which the return processes consistently depart from these models in theory as well as in its statistical properties. This paper gives a fundamental review of the development of a stock price model based on pure jump processes to capture the unique behavior exhibited by some stocks on the Exchange. Although pure jump processes have been examined thoroughly by other authors, there is a lack of mathematical clarity in terms of deriving the underlying stock price process. This paper provides a link between stock prices existing on a measure space to its development as a pure jump Levy process. We test the suitability of the model to the empirical evidence using numerical procedures. The simulation results show that the trajectories of the model are a better fit for the empirical data than those produced by the diffusion and jump diffusion models.
