Asymptotic Efficiencies of a Nonparametric Life Test for Smaller Percentiles of a Gamma Distribution
伽马分布较低分位点非参数寿命检验的渐近效率AI 解读 ↓
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伽马分布较低分位点非参数寿命检验的渐近效率
- 研究问题
- 在伽马分布寿命试验中，针对较低分位点使用符号检验及相应区间与点估计，能否在提前终止时保持较高效率？
- 方法与思路
- 作者分析已有符号检验类方法的估计与检验性质，并在仅部分试验品失效的条件下与参数方法比较效率。
- 材料陈述的贡献
- 摘要明确表示未提出新方法，而是论证既有非参数程序在某些寿命试验中的效率及节省时间或成本的可能性。
- 阅读关注点
- 应核对低分位点范围、停止试验规则、参数比较基准，以及渐近效率与摘要所述任意样本量判断之间的关系。
- 阅读边界
- 索引稿件版本未注明；摘要对适用总体与样本量的表述较宽，但未给出依据，不能据此宣称非参数方法普遍无效率损失。
原文摘要
This paper does not present new statistical methods. Rather, it shows that a well known nonparametric procedure which is valid under extremely general conditions also has high efficiency and other favorable properties for certain types of life testing situations. This nonparametric method is the sign test and its confidence interval and point estimate analogs. Sign test procedures and methods of applying them have already received extensive coverage in the literature (e.g., [2]). Consequently, in this paper emphasis is placed on fields of application instead of on methods of application. However, the basic methods for obtaining tests, confidence intervals, and point estimates of the sign test type are restated for convenience. The properties investigated are concerned with the estimation and testing of smaller population percentage points for the case of a sample from a gamma probability distribution. The investigations show that appropriate use of the sign test type of nonparametric tests and estimates sometimes can yield a saving in cost or time without loss of statistical efficiency, since the experiment can be stopped when only a fraction of the items being life tested have failed. The nonparametric results are found to be highly efficient compared to the “best” parametric results based on the same fraction of items failed for the case of small population percentage points; this conclusion appears to be valid for any sample size and for any reasonable type of statistical population.