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Confidence bands for the CDF when sampling from a finite population

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  • Frey, Jesse

Abstract

We develop two methods for obtaining a confidence band for the cumulative distribution function (CDF) based on a simple random sample from a finite population of known size. The methods are exact when the population contains no repeated values, and conservative otherwise. The first method consists of using a Kolmogorov-Smirnov-type band, and the second method consists of combining together separate, equal-coverage-probability confidence intervals for each ordered population value. Confidence bands obtained using either method yield simultaneous confidence intervals for all ordered population values. Coverage probabilities are computed using a new recursive algorithm.

Suggested Citation

  • Frey, Jesse, 2009. "Confidence bands for the CDF when sampling from a finite population," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4126-4132, October.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:12:p:4126-4132
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    Cited by:

    1. Frey, Jesse, 2016. "An exact Kolmogorov–Smirnov test for whether two finite populations are the same," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 65-71.
    2. Jiangyan Wang & Suojin Wang & Lijian Yang, 2016. "Simultaneous confidence bands for the distribution function of a finite population and of its superpopulation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(4), pages 692-709, December.
    3. Lijie Gu & Suojin Wang & Lijian Yang, 2019. "Simultaneous confidence bands for the distribution function of a finite population in stratified sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 983-1005, August.

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