Some probability inequalities are established for extended negatively dependent(END) random variables. The inequalities extend some corresponding ones for negatively associated random variables and negatively orthant ...Some probability inequalities are established for extended negatively dependent(END) random variables. The inequalities extend some corresponding ones for negatively associated random variables and negatively orthant dependent random variables. By using these probability inequalities, we further study the complete convergence for END random variables. We also obtain the convergence rate O(n-1/2ln1/2n) for the strong law of large numbers, which generalizes and improves the corresponding ones for some known results.展开更多
The tail probability inequalities for the sum of independent unbounded random variables on a probability space (Omega, T, P) were studied and a new method was proposed to treat the sum of independent unbounded random ...The tail probability inequalities for the sum of independent unbounded random variables on a probability space (Omega, T, P) were studied and a new method was proposed to treat the sum of independent unbounded random variables by truncating the original probability space (Omega, T, P). The probability exponential inequalities for sums of the results, some independent unbounded random variables were given. As applications of interesting examples were given. The examples show that the method proposed in the paper and the results of the paper are quite useful in the study of the large sample properties of the sums of independent unbounded random variables.展开更多
et X=(X1,...,Xn )' have a multivariate normal distribution with mean μ and covariance matrix Σ. In the case μ=0, Karlin and Rinott[6] obtained a necessary and sufficient condition on Σ for |X|=(|X1|,...,|Xn|)&...et X=(X1,...,Xn )' have a multivariate normal distribution with mean μ and covariance matrix Σ. In the case μ=0, Karlin and Rinott[6] obtained a necessary and sufficient condition on Σ for |X|=(|X1|,...,|Xn|)' to be MTP2. In this paper we consider the case μ≠0, and give some conditions under which |X| is MTP2. A necessary and sufficient condition is given for |X| to be TP2 when n=2 and μ≠0. Some results about the TP2 stochastic ordering are also given. The results are applied to obtain positive dependence and associated inequalities for multinormal and related distributions.展开更多
In this paper,a class of functionals of Kaplan-Meier estimator is investigated.Counting process martingale methods are used to show the asymptotic normality,and we establish a mean square error inequality and a probab...In this paper,a class of functionals of Kaplan-Meier estimator is investigated.Counting process martingale methods are used to show the asymptotic normality,and we establish a mean square error inequality and a probability inequality of them without the assumption that F,G are continuous,where F,G are survival time distribution and censoring time distribution respectively.展开更多
基金Supported by the Project of the Feature Specialty of China(TS11496)Supported by the Scientific Research Projects of Fuyang Teacher’s College(2009FSKJ09)
文摘Some probability inequalities are established for extended negatively dependent(END) random variables. The inequalities extend some corresponding ones for negatively associated random variables and negatively orthant dependent random variables. By using these probability inequalities, we further study the complete convergence for END random variables. We also obtain the convergence rate O(n-1/2ln1/2n) for the strong law of large numbers, which generalizes and improves the corresponding ones for some known results.
文摘The tail probability inequalities for the sum of independent unbounded random variables on a probability space (Omega, T, P) were studied and a new method was proposed to treat the sum of independent unbounded random variables by truncating the original probability space (Omega, T, P). The probability exponential inequalities for sums of the results, some independent unbounded random variables were given. As applications of interesting examples were given. The examples show that the method proposed in the paper and the results of the paper are quite useful in the study of the large sample properties of the sums of independent unbounded random variables.
文摘et X=(X1,...,Xn )' have a multivariate normal distribution with mean μ and covariance matrix Σ. In the case μ=0, Karlin and Rinott[6] obtained a necessary and sufficient condition on Σ for |X|=(|X1|,...,|Xn|)' to be MTP2. In this paper we consider the case μ≠0, and give some conditions under which |X| is MTP2. A necessary and sufficient condition is given for |X| to be TP2 when n=2 and μ≠0. Some results about the TP2 stochastic ordering are also given. The results are applied to obtain positive dependence and associated inequalities for multinormal and related distributions.
基金This project is supported by China Postdoctoral Science Foundation
文摘In this paper,a class of functionals of Kaplan-Meier estimator is investigated.Counting process martingale methods are used to show the asymptotic normality,and we establish a mean square error inequality and a probability inequality of them without the assumption that F,G are continuous,where F,G are survival time distribution and censoring time distribution respectively.
