Distribution-free tolerance intervals with nomination samples: Applications to mercury contamination in fish

Q Mathematics

Statistical Methodology Pub Date : 2015-09-01 DOI:10.1016/j.stamet.2015.03.002

Mohammad Nourmohammadi, Mohammad Jafari Jozani, Brad C. Johnson

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引用次数: 10

Abstract

Tolerance intervals are enclosure intervals which will cover a fixed portion of the population distribution with a specified confidence. These intervals are widely used in clinical, environmental, biological and industrial applications, including quality control and environmental monitoring, to help determine limits for detection or assessment monitoring. In many of these applications the measurement of the variable of interest is costly and/or destructive but a small number of sampling units can be ranked easily by using expert-opinion knowledge or inexpensive and easily obtained measurements from these units. In this paper, we construct tolerance intervals based on the expensive measurements that are obtained using randomized nomination sampling (RNS) with the help of inexpensive auxiliary information. We study the performance of our proposed RNS-based tolerance intervals based on the corresponding coverage probabilities and the necessary sample size for their existence with those based on simple random sampling (SRS). The efficiency of the constructed RNS-based tolerance intervals compared to their SRS counterparts is discussed. We investigate the performance of RNS-based tolerance intervals for different values of the design parameters and various population shapes. We find the values of the design parameters which improve RNS over SRS. The RNS design in presence of ranking error is discussed and a new method for estimating ranking error probabilities is proposed. Theoretical results are augmented with numerical evaluations and a case study based on a fish mercury level dataset.

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指定样品的无分布公差区间:在鱼类汞污染中的应用

容忍区间是封闭区间，它将以规定的置信度覆盖种群分布的固定部分。这些间隔广泛用于临床、环境、生物和工业应用，包括质量控制和环境监测，以帮助确定检测或评估监测的限度。在许多这样的应用中，对感兴趣的变量的测量是昂贵的和/或破坏性的，但是通过使用专家意见知识或从这些单位中廉价且容易获得的测量，可以很容易地对少数抽样单位进行排序。本文基于随机指定抽样(RNS)方法得到的昂贵的测量值，利用廉价的辅助信息构造公差区间。我们根据相应的覆盖概率及其存在的必要样本量与基于简单随机抽样(SRS)的容错区间研究了我们提出的基于rns的容错区间的性能。讨论了构建的基于rns的容错区间与基于SRS的容错区间的效率。我们研究了基于rs的公差区间在不同设计参数值和不同种群形状下的性能。我们找到了能使RNS优于SRS的设计参数值。讨论了存在排序误差的RNS设计，提出了一种估计排序误差概率的新方法。理论结果与数值评估和基于鱼类汞水平数据集的案例研究相结合。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistical Methodology STATISTICS & PROBABILITY-

CiteScore

0.59

自引率

0.00%

发文量

期刊介绍： Statistical Methodology aims to publish articles of high quality reflecting the varied facets of contemporary statistical theory as well as of significant applications. In addition to helping to stimulate research, the journal intends to bring about interactions among statisticians and scientists in other disciplines broadly interested in statistical methodology. The journal focuses on traditional areas such as statistical inference, multivariate analysis, design of experiments, sampling theory, regression analysis, re-sampling methods, time series, nonparametric statistics, etc., and also gives special emphasis to established as well as emerging applied areas.