Coverage Probabilities of Simultaneous Confidence Bands and Regions for Log-Location-Scale Distributions

Date
2011-01-01
Authors
Hong, Yili
Escobar, Luis
Meeker, William
Meeker, William
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Altmetrics
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Statistics
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Statistics
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 SCB for the cdf of a continuous random variable derived from a 100(1−α)% 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−α). This paper identifies the conditions under which the coverage probability for the SCB procedure is exactly (1−α). A small simulation illustrates the important theoretical results in the paper.

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This preprint was published as Yili Hong, Luis A. Escobar, William Q. Meeker, "Coverage Probabilities of Simultaneous Confidence Bands and Regions for Log-Location-Scale Distributions", Statistics and Probability Letters (2010): 733-738, doi: 10.1016/j.spl.2010.01.003.

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