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Coverage probabilities of simultaneous confidence bands and regions for log-location-scale distributions

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  • Hong, Yili
  • Escobar, Luis A.
  • Meeker, William Q.

Abstract

A simultaneous confidence band (SCB) for the cumulative distribution function (cdf) of a random variable can be used to assess the statistical uncertainty of the estimated cdf. Cheng and Iles (1983) presented a general approach of constructing an SCBÂ for the cdf of a continuous random variable derived from a 100(1-[alpha])% simultaneous confidence region (SCR) for the parameters of the distribution. The Cheng and Iles SCB procedure includes the true cdf with probability at least (1-[alpha]). This paper identifies the conditions under which the coverage probability for the SCB procedure is exactly (1-[alpha]). A small simulation illustrates the important theoretical results in the paper.

Suggested Citation

  • Hong, Yili & Escobar, Luis A. & Meeker, William Q., 2010. "Coverage probabilities of simultaneous confidence bands and regions for log-location-scale distributions," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 733-738, April.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:7-8:p:733-738
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    Cited by:

    1. Jie Min & Yili Hong & Caleb B. King & William Q. Meeker, 2022. "Reliability analysis of artificial intelligence systems using recurrent events data from autonomous vehicles," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(4), pages 987-1013, August.
    2. Dag Kolsrud, 2015. "A Time‐Simultaneous Prediction Box for a Multivariate Time Series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(8), pages 675-693, December.
    3. Fabian Mies & Stefan Bedbur, 2017. "On the coverage probabilities of parametric confidence bands for continuous distribution and quantile functions constructed via confidence regions for a location-scale parameter," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(4), pages 925-944, August.

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