The presence of dispersion/variability in any process is understood and its careful monitoring may furnish the performance of any process. The interquartile range (IQR) is one of the dispersion measures based on lower...The presence of dispersion/variability in any process is understood and its careful monitoring may furnish the performance of any process. The interquartile range (IQR) is one of the dispersion measures based on lower and upper quartiles. For efficient monitoring of process dispersion, we have proposed auxiliary information based Shewhart-type IQR control charts (namely IQRr and IQRp charts) based on ratio and product estimators of lower and upper quartiles under bivariate normally distributed process. We have developed the control structures of proposed charts and compared their performances with the usual IQR chart in terms of detection ability of shift in process dispersion. For the said purpose power curves are constructed to demonstrate the performance of the three IQR charts under discussion in this article. We have also provided an illustrative example to justify theory and finally closed with concluding remarks.展开更多
G-Brownian motion has a very rich and interesting new structure that nontrivially generalizes the classical Brownian motion.Its quadratic variation process is also a continuous process with independent and stationary ...G-Brownian motion has a very rich and interesting new structure that nontrivially generalizes the classical Brownian motion.Its quadratic variation process is also a continuous process with independent and stationary increments.We prove a self-normalized functional central limit theorem for independent and identically distributed random variables under the sub-linear expectation with the limit process being a G-Brownian motion self-normalized by its quadratic variation.To prove the self-normalized central limit theorem,we also establish a new Donsker’s invariance principle with the limit process being a generalized G-Brownian motion.展开更多
Let {Xm（t）, t∈R＋} be an m-Fold integrated Brownian motion. In this paper, with the help of small ball probability estimate, a functional law of the iterated logarithm （LIL） for Xm（t） is established. This exten...Let {Xm（t）, t∈R＋} be an m-Fold integrated Brownian motion. In this paper, with the help of small ball probability estimate, a functional law of the iterated logarithm （LIL） for Xm（t） is established. This extends the classic Chung type liminf result for this process. Furthermore, a result about the weighted occupation measure for Xm（t） is also obtained.展开更多
文摘The presence of dispersion/variability in any process is understood and its careful monitoring may furnish the performance of any process. The interquartile range (IQR) is one of the dispersion measures based on lower and upper quartiles. For efficient monitoring of process dispersion, we have proposed auxiliary information based Shewhart-type IQR control charts (namely IQRr and IQRp charts) based on ratio and product estimators of lower and upper quartiles under bivariate normally distributed process. We have developed the control structures of proposed charts and compared their performances with the usual IQR chart in terms of detection ability of shift in process dispersion. For the said purpose power curves are constructed to demonstrate the performance of the three IQR charts under discussion in this article. We have also provided an illustrative example to justify theory and finally closed with concluding remarks.
基金Research supported by Grants from the National Natural Science Foundation of China(No.11225104)the 973 Program(No.2015CB352302)and the Fundamental Research Funds for the Central Universities.
文摘G-Brownian motion has a very rich and interesting new structure that nontrivially generalizes the classical Brownian motion.Its quadratic variation process is also a continuous process with independent and stationary increments.We prove a self-normalized functional central limit theorem for independent and identically distributed random variables under the sub-linear expectation with the limit process being a G-Brownian motion self-normalized by its quadratic variation.To prove the self-normalized central limit theorem,we also establish a new Donsker’s invariance principle with the limit process being a generalized G-Brownian motion.
基金Project supported by the National Natural Science Foundation of China (No.10131040)the Specialized Research Fund for the Doctor Program of Higher Education (No.2002335090).
文摘Let {Xm（t）, t∈R＋} be an m-Fold integrated Brownian motion. In this paper, with the help of small ball probability estimate, a functional law of the iterated logarithm （LIL） for Xm（t） is established. This extends the classic Chung type liminf result for this process. Furthermore, a result about the weighted occupation measure for Xm（t） is also obtained.
