摘要:
基于本文中提出的新截尾试验方案---双定时混合截尾, 得到了两参数Pareto分布参数的极大似然估计,根据Fisher信息量推导出参数\theta的渐近置信区间.当\alpha已知时, 取Gamma先验分布的情况下,求出了不同损失函数下参数\theta的Bayes和E-Bayes估计以及可靠度函数的Bayes估计. 当\alpha,\theta都未知时,取联合无信息先验分布, 在平方误差损失函数下计算出\alpha,\theta的Bayes估计. 利用蒙特卡洛方法模拟出双定时混合截尾样本,得到了未知参数及可靠度函数的估计, 并计算出相对误差,随着样本量的增加相对误差和置信区间的长度逐渐减小.最后对一个数值例子进行了统计分析.
Abstract:
Based on a new lifetime testing scheme proposed in this paper, that is, double type-I hybrid censoring scheme, the maximum likelihood estimates of the parameters are obtained for two-parameter Pareto distribution. Also, the asymptotic confidence interval of \theta is obtained from Fisher information. When \alpha is known, the Bayesian and E-Bayesian estimates of \theta, as well as the Bayesian estimates of reliability function under different loss functions are obtained using the Gamma prior distribution. When both \alpha and \theta are unknown, the joint noninformation prior distribution is taken, and the Bayesian estimates of \alpha and \theta are calculated under the squared error loss function. Using Monte Carlo method to simulate the double type-I hybrid censored samples, the estimates of the unknown parameters and reliability function are obtained, with the increase of the sample size, the relative errors and the lengths of the confidence interval decrease gradually. Finally, a numerical example is analyzed.
百度学术
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