Simultaneous Inferences on the Cumulative Distribution Function of a Normal Distribution

A. J. Hayter, S. Kiatsupaibul, P. Napalai and W. Liu

Communications in Statistics - Theory and Methods, 2015, vol. 44, issue 24, 5136-5145

Abstract: This paper addresses the problem of constructing simultaneous confidence intervals for the cumulative distribution function of a normal distribution at several specified points. The procedure is based upon the observation of a random sample of independent observations from a normal distribution with an unknown mean and variance. A new methodology is proposed for obtaining confidence intervals with a specified overall simultaneous confidence level through the inversion of acceptance sets. Both one-sided and two-sided confidence intervals are considered. Some illustrations of the new method are provided, and comparisons are made with other approaches to the problem.

Date: 2015
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DOI: 10.1080/03610926.2013.815206

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