标题： Ranked集抽样中熵的改进估计量和拟合优度检验 显示英文标题

标题： Improved estimator of the entropy and goodness of fit tests in ranked set sampling

摘要： 熵是许多统计学和工程学问题中最常用的一种不确定性度量方法。 在统计文献中，熵用于计算 Kullback-Leibler (KL) 信息，这是执行拟合优度检验的一种强大工具。 排名集抽样（RSS）似乎能够为文献中大量研究的问题提供改进的总体参数估计量。 它适用于感兴趣变量难以测量或成本高昂的情况，但在小样本中排序却相对容易。 本文引入了两个熵的估计量，并与其他估计量以及简单随机抽样（SRS）中的熵估计量在偏差和均方根误差（RMSE）的意义上进行了比较。 观察到 RSS 方案可以改善该估计量。 使用熵的最佳估计量与基于 RSS 方案的均值估计量以及两个偏倚和无偏的方差估计量，来估算 KL 信息并执行指数分布和正态分布的拟合优度检验。 所需的临界值和功效被计算出来。 还观察到 RSS 估计量会提高功效。 显示英文摘要

摘要： The entropy is one of the most applicable uncertainty measures in many statistical and en- gineering problems. In statistical literature, the entropy is used in calculation of the Kullback- Leibler (KL) information which is a powerful mean for performing goodness of fit tests. Ranked Set Sampling (RSS) seems to provide improved estimators of many parameters of the popu- lation in the huge studied problems in the literature. It is developed for situations where the variable of interest is difficult or expensive to measure, but where ranking in small sub-samples is easy. In This paper, we introduced two estimators for the entropy and compare them with each other and the estimator of the entropy in Simple Random Sampling (SRS) in the sense of bias and Root of Mean Square Errors (RMSE). It is observed that the RSS scheme would improve this estimator. The best estimator of the entropy is used along with the estimator of the mean and two biased and unbiased estimators of variance based on RSS scheme, to esti- mate the KL information and perform goodness of fit tests for exponentiality and normality. The desired critical values and powers are calculated. It is also observed that RSS estimators would increase powers.