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

Hong, Yili; Escobar, Luis; Meeker, William; Meeker, William

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

File

2011_MeekerWQ_CoverageProbabilitiesSimultaneous.pdf (215.55 KB)

Date

2011-01-01

Authors

Hong, Yili

Escobar, Luis

Meeker, William

Authors

Person

Meeker, William

Distinguished Professor

Organizational Units

Organizational Unit

Statistics

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Department

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.

Comments

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.