排序集抽样下指数分布的产品可靠度研究

为了提高指数分布产品可靠度的估计效率,研究了基于排序集抽样方法的极大似然估计量(Maximum likelihood estimator,MLE),证明了新MLE具有存在性、唯一性和渐近正态性,并通过排序集样本的Fisher信息得到MLE的渐近方差。针对似然方程没有显式解的问题,利用部分期望法对MLE进行修正,并给出其具体表达式。渐近相对效率和模拟相对效率的研究结果表明:排序集抽样下MLE和修正MLE的估计效率都一致高于简单随机抽样下MLE。最后,将推荐方法应用到转移性肾癌的临床研究中。

Research on Product Reliability for Exponential Distribution Based on Ranked Set Sampling

In order to improve the estimation efficiency of the product reliability for exponential distribution, this paper considers the maximum likelihood estimator(MLE)based on ranked set sampling. The proposed MLE is shown to have existence, uniqueness and asymptotic normality, and its asymptotic variance is obtained by the Fisher information of ranked set sampte. However, the root of likelihood equation cannot be written in closed form. Therefore, the modified MLE having closed from is proposed using the technique replaced some terms in the likelihood equation by their expectations. The values of asymptotic relative efficiency and simulated relative efficiency show that the proposed MLE and modified MLE are always more efficient than the MLE using simple random sampling. Finally, the proposed method is applied to a clinical study on metastatic renal carcinoma.