Let I be the set of all infinitely divisible random variables with finite second moments,I_(0)={X∈I;Var(X)>0},P_(I)=inf_(x∈I)P{|X-E[X]|≤√Var(X)}and P_(I_(0))=inf P{|X-E[X]|<√Var(X)}.Firstly,we prove that P_...Let I be the set of all infinitely divisible random variables with finite second moments,I_(0)={X∈I;Var(X)>0},P_(I)=inf_(x∈I)P{|X-E[X]|≤√Var(X)}and P_(I_(0))=inf P{|X-E[X]|<√Var(X)}.Firstly,we prove that P_(I)≥P_(I_(0))>0.Secondly,we find_(x∈I_(0))the exact values of inf P{|X-E[X]|≤√Var(X)}and inf P{|X-E[X]|<√Var(X)}for the cases that J is the set of all geometric random variables,symmetric geometric random variables,Poisson random variables and symmetric Poisson random variables,respectively.As a consequence,we obtain that P_(I)≤e^(-1)^(∞)∑_(k=0)1/2^(2k)(k!)^(2)≈0.46576 and P_(I_(0))≤e^(-1)≈0.36788.展开更多
Complementary exponential geometric distribution has many applications in survival and reliability analysis.Due to its importance,in this study,we are aiming to estimate the parameters of this model based on progressi...Complementary exponential geometric distribution has many applications in survival and reliability analysis.Due to its importance,in this study,we are aiming to estimate the parameters of this model based on progressive type-II censored observations.To do this,we applied the stochastic expectation maximization method and Newton-Raphson techniques for obtaining the maximum likelihood estimates.We also considered the estimation based on Bayesian method using several approximate:MCMC samples,Lindely approximation and Metropolis-Hasting algorithm.In addition,we considered the shrinkage estimators based on Bayesian and maximum likelihood estimators.Then,the HPD intervals for the parameters are constructed based on the posterior samples from the Metropolis-Hasting algorithm.In the sequel,we obtained the performance of different estimators in terms of biases,estimated risks and Pitman closeness via Monte Carlo simulation study.This paper will be ended up with a real data set example for illustration of our purpose.展开更多
Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is...Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is to learn the kernel from the data automatically. A general regularized risk functional （RRF） criterion for kernel matrix learning is proposed. Compared with the RRF criterion, general RRF criterion takes into account the geometric distributions of the embedding data points. It is proven that the distance between different geometric distdbutions can be estimated by their centroid distance in the reproducing kernel Hilbert space. Using this criterion for kernel matrix learning leads to a convex quadratically constrained quadratic programming （QCQP） problem. For several commonly used loss functions, their mathematical formulations are given. Experiment results on a collection of benchmark data sets demonstrate the effectiveness of the proposed method.展开更多
Cloud computing is an increasingly popular paradigm for accessing computing resources. For marketing application, this paper proposes a dynamic model of customer interpurchase time with geometric distribution. This mo...Cloud computing is an increasingly popular paradigm for accessing computing resources. For marketing application, this paper proposes a dynamic model of customer interpurchase time with geometric distribution. This model considers that there is a change point in interpurchase time and two types of probability density functions are demonstrated （time decreasing before changing; time increasing after changing）. With the description of change point, Bernoulli and Poisson distributions also are discussed in the model construction.展开更多
基金supported by the National Natural Science Foundation of China(12161029,12171335)the National Natural Science Foundation of Hainan Province(121RC149)+1 种基金the Science Development Project of Sichuan University(2020SCUNL201)the Natural Sciences and Engineering Research Council of Canada(4394-2018).
文摘Let I be the set of all infinitely divisible random variables with finite second moments,I_(0)={X∈I;Var(X)>0},P_(I)=inf_(x∈I)P{|X-E[X]|≤√Var(X)}and P_(I_(0))=inf P{|X-E[X]|<√Var(X)}.Firstly,we prove that P_(I)≥P_(I_(0))>0.Secondly,we find_(x∈I_(0))the exact values of inf P{|X-E[X]|≤√Var(X)}and inf P{|X-E[X]|<√Var(X)}for the cases that J is the set of all geometric random variables,symmetric geometric random variables,Poisson random variables and symmetric Poisson random variables,respectively.As a consequence,we obtain that P_(I)≤e^(-1)^(∞)∑_(k=0)1/2^(2k)(k!)^(2)≈0.46576 and P_(I_(0))≤e^(-1)≈0.36788.
文摘Complementary exponential geometric distribution has many applications in survival and reliability analysis.Due to its importance,in this study,we are aiming to estimate the parameters of this model based on progressive type-II censored observations.To do this,we applied the stochastic expectation maximization method and Newton-Raphson techniques for obtaining the maximum likelihood estimates.We also considered the estimation based on Bayesian method using several approximate:MCMC samples,Lindely approximation and Metropolis-Hasting algorithm.In addition,we considered the shrinkage estimators based on Bayesian and maximum likelihood estimators.Then,the HPD intervals for the parameters are constructed based on the posterior samples from the Metropolis-Hasting algorithm.In the sequel,we obtained the performance of different estimators in terms of biases,estimated risks and Pitman closeness via Monte Carlo simulation study.This paper will be ended up with a real data set example for illustration of our purpose.
基金supported by the National Natural Science Fundation of China (60736021)the Joint Funds of NSFC-Guangdong Province(U0735003)
文摘Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is to learn the kernel from the data automatically. A general regularized risk functional （RRF） criterion for kernel matrix learning is proposed. Compared with the RRF criterion, general RRF criterion takes into account the geometric distributions of the embedding data points. It is proven that the distance between different geometric distdbutions can be estimated by their centroid distance in the reproducing kernel Hilbert space. Using this criterion for kernel matrix learning leads to a convex quadratically constrained quadratic programming （QCQP） problem. For several commonly used loss functions, their mathematical formulations are given. Experiment results on a collection of benchmark data sets demonstrate the effectiveness of the proposed method.
基金supported by the National Science Council of Taiwan under Grant No. NSC 99-2410-H-156-013 and NSC 98-2410-H-156-021
文摘Cloud computing is an increasingly popular paradigm for accessing computing resources. For marketing application, this paper proposes a dynamic model of customer interpurchase time with geometric distribution. This model considers that there is a change point in interpurchase time and two types of probability density functions are demonstrated （time decreasing before changing; time increasing after changing）. With the description of change point, Bernoulli and Poisson distributions also are discussed in the model construction.
