Reliability analysis is the key to evaluate software’s quality. Since the early 1970s, the Power Law Process, among others, has been used to assess the rate of change of software reliability as time-varying function ...Reliability analysis is the key to evaluate software’s quality. Since the early 1970s, the Power Law Process, among others, has been used to assess the rate of change of software reliability as time-varying function by using its intensity function. The Bayesian analysis applicability to the Power Law Process is justified using real software failure times. The choice of a loss function is an important entity of the Bayesian settings. The analytical estimate of likelihood-based Bayesian reliability estimates of the Power Law Process under the squared error and Higgins-Tsokos loss functions were obtained for different prior knowledge of its key parameter. As a result of a simulation analysis and using real data, the Bayesian reliability estimate under the Higgins-Tsokos loss function not only is robust as the Bayesian reliability estimate under the squared error loss function but also performed better, where both are superior to the maximum likelihood reliability estimate. A sensitivity analysis resulted in the Bayesian estimate of the reliability function being sensitive to the prior, whether parametric or non-parametric, and to the loss function. An interactive user interface application was additionally developed using Wolfram language to compute and visualize the Bayesian and maximum likelihood estimates of the intensity and reliability functions of the Power Law Process for a given data.展开更多
In this paper, we consider the problem of determining the order ofINAR（Q） model on the basis of the Bayesian estimation theory. The Bayesian es-timator for the order is given with respect to a squared-error loss fu...In this paper, we consider the problem of determining the order ofINAR（Q） model on the basis of the Bayesian estimation theory. The Bayesian es-timator for the order is given with respect to a squared-error loss function. The consistency of the estimator is discussed. The results of a simulation study for the estimation method are presented.展开更多
A modification of ranked set sampling (RSS) called maximum ranked set sampling with unequal sample (MRSSU) is considered for the Bayesian estimation of scale parameter α of the Weibull distribution. Under this method...A modification of ranked set sampling (RSS) called maximum ranked set sampling with unequal sample (MRSSU) is considered for the Bayesian estimation of scale parameter α of the Weibull distribution. Under this method, we use Linex loss function, conjugate and Jeffreys prior distributions to derive the Bayesian estimate of α. In order to measure the efficiency of the obtained Bayesian estimates with respect to the Bayesian estimates of simple random sampling (SRS), we compute the bias, mean squared error (MSE) and asymptotic relative efficiency of the obtained Bayesian estimates using simulation. It is shown that the proposed estimates are found to be more efficient than the corresponding one based on SRS.展开更多
The risk decision of small multi-frequency investment mode of agricultural products is studied based on Bayesian method. This method can take advantage of new market information reasonably,analyze the posterior risk a...The risk decision of small multi-frequency investment mode of agricultural products is studied based on Bayesian method. This method can take advantage of new market information reasonably,analyze the posterior risk and quantify the decision risk. It provides a scientific way for the risk decision of agricultural enterprises and is advantageous to enhancing the benefit of project.展开更多
利用刀切法和Bayes估计方法,在加权平方损失函数下,得到Rayleigh分布在选取先验分布为Jefferys无信息分布和Gamma分布的情况下参数的Bayes估计的精确形式,在此基础上进一步研究了参数的刀切Bayes估计.最后在R软件中运用MCMC(Markov Chai...利用刀切法和Bayes估计方法,在加权平方损失函数下,得到Rayleigh分布在选取先验分布为Jefferys无信息分布和Gamma分布的情况下参数的Bayes估计的精确形式,在此基础上进一步研究了参数的刀切Bayes估计.最后在R软件中运用MCMC(Markov Chain Monte Carlo)算法对Rayleigh分布参数的Bayes估计和刀切Bayes估计进行数值模拟.模拟结果显示:当样本容量较大时,相同先验分布下刀切Bayes估计模拟效果更好.展开更多
文摘Reliability analysis is the key to evaluate software’s quality. Since the early 1970s, the Power Law Process, among others, has been used to assess the rate of change of software reliability as time-varying function by using its intensity function. The Bayesian analysis applicability to the Power Law Process is justified using real software failure times. The choice of a loss function is an important entity of the Bayesian settings. The analytical estimate of likelihood-based Bayesian reliability estimates of the Power Law Process under the squared error and Higgins-Tsokos loss functions were obtained for different prior knowledge of its key parameter. As a result of a simulation analysis and using real data, the Bayesian reliability estimate under the Higgins-Tsokos loss function not only is robust as the Bayesian reliability estimate under the squared error loss function but also performed better, where both are superior to the maximum likelihood reliability estimate. A sensitivity analysis resulted in the Bayesian estimate of the reliability function being sensitive to the prior, whether parametric or non-parametric, and to the loss function. An interactive user interface application was additionally developed using Wolfram language to compute and visualize the Bayesian and maximum likelihood estimates of the intensity and reliability functions of the Power Law Process for a given data.
文摘In this paper, we consider the problem of determining the order ofINAR（Q） model on the basis of the Bayesian estimation theory. The Bayesian es-timator for the order is given with respect to a squared-error loss function. The consistency of the estimator is discussed. The results of a simulation study for the estimation method are presented.
文摘A modification of ranked set sampling (RSS) called maximum ranked set sampling with unequal sample (MRSSU) is considered for the Bayesian estimation of scale parameter α of the Weibull distribution. Under this method, we use Linex loss function, conjugate and Jeffreys prior distributions to derive the Bayesian estimate of α. In order to measure the efficiency of the obtained Bayesian estimates with respect to the Bayesian estimates of simple random sampling (SRS), we compute the bias, mean squared error (MSE) and asymptotic relative efficiency of the obtained Bayesian estimates using simulation. It is shown that the proposed estimates are found to be more efficient than the corresponding one based on SRS.
基金Supported by Intelligent Logistics System of Beijing Key Laboratory(BZ0211)039 Specialty Construction-Professional Group Construction at Municipal Level(PXM2015-014214-000039)
文摘The risk decision of small multi-frequency investment mode of agricultural products is studied based on Bayesian method. This method can take advantage of new market information reasonably,analyze the posterior risk and quantify the decision risk. It provides a scientific way for the risk decision of agricultural enterprises and is advantageous to enhancing the benefit of project.
文摘利用刀切法和Bayes估计方法,在加权平方损失函数下,得到Rayleigh分布在选取先验分布为Jefferys无信息分布和Gamma分布的情况下参数的Bayes估计的精确形式,在此基础上进一步研究了参数的刀切Bayes估计.最后在R软件中运用MCMC(Markov Chain Monte Carlo)算法对Rayleigh分布参数的Bayes估计和刀切Bayes估计进行数值模拟.模拟结果显示:当样本容量较大时,相同先验分布下刀切Bayes估计模拟效果更好.
