This paper considers the Bayesian and expected Bayesian（E-Bayesian） estimations of the parameter and reliability function for competing risk model from Gompertz distribution under Type-I progressively hybrid censori...This paper considers the Bayesian and expected Bayesian（E-Bayesian） estimations of the parameter and reliability function for competing risk model from Gompertz distribution under Type-I progressively hybrid censoring scheme（PHCS）. The estimations are obtained based on Gamma conjugate prior for the parameter under squared error（SE） and Linex loss functions. The simulation results are provided for the comparison purpose and one data set is analyzed.展开更多
This paper develops a new method, named E-Bayesian estimation method, to estimate the reliability parameters. The E-Bayesian estimation method of the reliability are derived for the zero-failure data from the product ...This paper develops a new method, named E-Bayesian estimation method, to estimate the reliability parameters. The E-Bayesian estimation method of the reliability are derived for the zero-failure data from the product with Binomial distribution. Firstly, for the product reliability, the definitions of E-Bayesian estimation were given, and on the base, expressions of the E-Bayesian estimation and hierarchical Bayesian estimation of the products reliability was given. Secondly, discuss properties of the E-Bayesian estimation. Finally, the new method is applied to a real zero-failure data set, and as can be seen, it is both efficient and easy to operate.展开更多
In this present work,we propose the expected Bayesian and hierarchical Bayesian approaches to estimate the shape parameter and hazard rate under a generalized progressive hybrid censoring scheme for the Kumaraswamy di...In this present work,we propose the expected Bayesian and hierarchical Bayesian approaches to estimate the shape parameter and hazard rate under a generalized progressive hybrid censoring scheme for the Kumaraswamy distribution.These estimates have been obtained using gamma priors based on various loss functions such as squared error,entropy,weighted balance,and minimum expected loss functions.An investigation is carried out using Monte Carlo simulation to evaluate the effectiveness of the suggested estimators.The simulation provides a quantitative assessment of the estimates accuracy and efficiency under various conditions by comparing them in terms of mean squared error.Additionally,the monthly water capacity of the Shasta reservoir is examined to offer real-world examples of how the suggested estimations may be used and performed.展开更多
为了度量E-Bayes估计的误差,该文基于E-Bayes估计的定义,引入了E-Bayes估计的E-MSE(expected mean square error)的定义.对Poisson分布的参数,在不同损失函数(包括:平方损失,K-损失,加权平方损失)下分别给出了E-Bayes估计及其E-MSE的表...为了度量E-Bayes估计的误差,该文基于E-Bayes估计的定义,引入了E-Bayes估计的E-MSE(expected mean square error)的定义.对Poisson分布的参数,在不同损失函数(包括:平方损失,K-损失,加权平方损失)下分别给出了E-Bayes估计及其E-MSE的表达式.用MonteCarlo方法进行模拟比较提出的估计方法的性能,分析了一个真实数据集并进行了比较,所得结果比较基于E-MSE,结果表明该文提出的方法可行且便于应用.展开更多
基金supported by the National Natural Science Foundation of China(7117116471401134+1 种基金71571144)the Natural Science Basic Research Program of Shaanxi Province(2015JM1003)
文摘This paper considers the Bayesian and expected Bayesian（E-Bayesian） estimations of the parameter and reliability function for competing risk model from Gompertz distribution under Type-I progressively hybrid censoring scheme（PHCS）. The estimations are obtained based on Gamma conjugate prior for the parameter under squared error（SE） and Linex loss functions. The simulation results are provided for the comparison purpose and one data set is analyzed.
基金Supported by the Fujian Province NSFC(2009J01001)
文摘This paper develops a new method, named E-Bayesian estimation method, to estimate the reliability parameters. The E-Bayesian estimation method of the reliability are derived for the zero-failure data from the product with Binomial distribution. Firstly, for the product reliability, the definitions of E-Bayesian estimation were given, and on the base, expressions of the E-Bayesian estimation and hierarchical Bayesian estimation of the products reliability was given. Secondly, discuss properties of the E-Bayesian estimation. Finally, the new method is applied to a real zero-failure data set, and as can be seen, it is both efficient and easy to operate.
基金funded by Researchers Supporting Project number(RSPD2025R969),King Saud University,Riyadh,Saudi Arabia.
文摘In this present work,we propose the expected Bayesian and hierarchical Bayesian approaches to estimate the shape parameter and hazard rate under a generalized progressive hybrid censoring scheme for the Kumaraswamy distribution.These estimates have been obtained using gamma priors based on various loss functions such as squared error,entropy,weighted balance,and minimum expected loss functions.An investigation is carried out using Monte Carlo simulation to evaluate the effectiveness of the suggested estimators.The simulation provides a quantitative assessment of the estimates accuracy and efficiency under various conditions by comparing them in terms of mean squared error.Additionally,the monthly water capacity of the Shasta reservoir is examined to offer real-world examples of how the suggested estimations may be used and performed.
基金山东省自然科学基金(the Natural Science Foundation of Shandong Province of China under Grant No.Y2006G20)山东省科技公关计划(the Key Technologies R&D Program of Shandong Province of China under Grant No.053120126)
文摘为了度量E-Bayes估计的误差,该文基于E-Bayes估计的定义,引入了E-Bayes估计的E-MSE(expected mean square error)的定义.对Poisson分布的参数,在不同损失函数(包括:平方损失,K-损失,加权平方损失)下分别给出了E-Bayes估计及其E-MSE的表达式.用MonteCarlo方法进行模拟比较提出的估计方法的性能,分析了一个真实数据集并进行了比较,所得结果比较基于E-MSE,结果表明该文提出的方法可行且便于应用.
