Let (X 1,X 2,...,X n) and (Y 1,Y 2,...,Y n) be real random vectors with the same marginal distributions,if (X 1,X 2,...,X n)≤ c(Y 1,Y 2,...,Y n), it is showed in this paper that ∑ n i=1 X i≤ c...Let (X 1,X 2,...,X n) and (Y 1,Y 2,...,Y n) be real random vectors with the same marginal distributions,if (X 1,X 2,...,X n)≤ c(Y 1,Y 2,...,Y n), it is showed in this paper that ∑ n i=1 X i≤ cx ∑ n i=1 Y i and max 1≤k≤n ∑ k i=1 X i≤ icx max 1≤k≤n ∑ k i=1 Y i hold.Based on this fact,a more general comparison theorem is obtained.展开更多
The purpose of this paper is to discuss the closure properties of increasing convex average order and NBUCA life distributions. Under the assumption that the units are only independent, characterizations of NBUCA clas...The purpose of this paper is to discuss the closure properties of increasing convex average order and NBUCA life distributions. Under the assumption that the units are only independent, characterizations of NBUCA class of life distributions are given. It is shown that NBUCA class is closed under the random maxima and the formation of parallel systems of independent units. As an application of the main results, the behavior of this class is developed in terms of the monotonicity of the residual life of k-out-of n systems given the time at which the （n -k ）-th failure has occurred.展开更多
Some new results about the NBU(2) class of life distributions were obtained. Fir stly, it was proved that the decrease with time of the increasing concave orderi ng of the excess lifetime in a renewal process leads to...Some new results about the NBU(2) class of life distributions were obtained. Fir stly, it was proved that the decrease with time of the increasing concave orderi ng of the excess lifetime in a renewal process leads to the NBU(2) property of t he interarrival times. Secondly, the NBU(2) class of life distributions is prove d to be closed under the formation of series systems. Finally, it was also shown that the NBU(2) class is closed under convolution operation.展开更多
It is proved that the right spread order is closed under the formation of parallel systems with independent and identical components. As an application,the simple upper bounds for both the mean and the variance of the...It is proved that the right spread order is closed under the formation of parallel systems with independent and identical components. As an application,the simple upper bounds for both the mean and the variance of the life length of a parallel system with independent and identical NBUE components are obtained. Furthermore,it is proved that the right spread order is also closed under increasing convex transformations under some conditions.展开更多
A new nonparametric procedure is developed to test the exponentiality against the strict NBUC property of a life distribution. The exact null distribution is derived by the theory of sample spacings, and the asymptoti...A new nonparametric procedure is developed to test the exponentiality against the strict NBUC property of a life distribution. The exact null distribution is derived by the theory of sample spacings, and the asymptotic normality is also established by the large sample theory of L-statistics. Finally, the lower and upper tailed probability of the exact null distribution and some numerical simulation results are presented as well.展开更多
The edges between vertices in networks take not only the common binary values, but also the ordered values in some situations(e.g., the measurement of the relationship between people from worst to best in social netwo...The edges between vertices in networks take not only the common binary values, but also the ordered values in some situations(e.g., the measurement of the relationship between people from worst to best in social networks). In this paper, the authors study the asymptotic property of the moment estimator based on the degrees of vertices in ordered networks whose edges are ordered random variables. In particular, the authors establish the uniform consistency and the asymptotic normality of the moment estimator when the number of parameters goes to infinity. Simulations and a real data example are provided to illustrate asymptotic results.展开更多
基金the National Natural Science Foundation of China( 1 0 371 1 0 9)
文摘Let (X 1,X 2,...,X n) and (Y 1,Y 2,...,Y n) be real random vectors with the same marginal distributions,if (X 1,X 2,...,X n)≤ c(Y 1,Y 2,...,Y n), it is showed in this paper that ∑ n i=1 X i≤ cx ∑ n i=1 Y i and max 1≤k≤n ∑ k i=1 X i≤ icx max 1≤k≤n ∑ k i=1 Y i hold.Based on this fact,a more general comparison theorem is obtained.
基金The Science Foundation of Shaanxi Pro-vincial Educational Department (06JK325)
文摘The purpose of this paper is to discuss the closure properties of increasing convex average order and NBUCA life distributions. Under the assumption that the units are only independent, characterizations of NBUCA class of life distributions are given. It is shown that NBUCA class is closed under the random maxima and the formation of parallel systems of independent units. As an application of the main results, the behavior of this class is developed in terms of the monotonicity of the residual life of k-out-of n systems given the time at which the （n -k ）-th failure has occurred.
文摘Some new results about the NBU(2) class of life distributions were obtained. Fir stly, it was proved that the decrease with time of the increasing concave orderi ng of the excess lifetime in a renewal process leads to the NBU(2) property of t he interarrival times. Secondly, the NBU(2) class of life distributions is prove d to be closed under the formation of series systems. Finally, it was also shown that the NBU(2) class is closed under convolution operation.
文摘It is proved that the right spread order is closed under the formation of parallel systems with independent and identical components. As an application,the simple upper bounds for both the mean and the variance of the life length of a parallel system with independent and identical NBUE components are obtained. Furthermore,it is proved that the right spread order is also closed under increasing convex transformations under some conditions.
基金This research is supported by the National Natural Science Foundation of Chinaunder Grant No. 10201010 and TY 10126014.
文摘A new nonparametric procedure is developed to test the exponentiality against the strict NBUC property of a life distribution. The exact null distribution is derived by the theory of sample spacings, and the asymptotic normality is also established by the large sample theory of L-statistics. Finally, the lower and upper tailed probability of the exact null distribution and some numerical simulation results are presented as well.
基金supported by the National Natural Science Foundation of China under Grant Nos.11271147,11471135partially supported by the National Natural Science Foundation of China under Grant No.11401239+1 种基金Funds of CCNU from the Colleges’s Basic Research and Operation of MOE(CCNU15A02032,CCNU15ZD011)a Fund from KLAS(130026507)
文摘The edges between vertices in networks take not only the common binary values, but also the ordered values in some situations(e.g., the measurement of the relationship between people from worst to best in social networks). In this paper, the authors study the asymptotic property of the moment estimator based on the degrees of vertices in ordered networks whose edges are ordered random variables. In particular, the authors establish the uniform consistency and the asymptotic normality of the moment estimator when the number of parameters goes to infinity. Simulations and a real data example are provided to illustrate asymptotic results.
