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Simultaneous Inferences on the Cumulative Distribution Function of a Normal Distribution |
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| Authors: | A. J. Hayter S. Kiatsupaibul P. Napalai W. Liu |
| Affiliation: | 1. Department of Business Information and Analytics, University of Denver, Denver, CO, USAAnthony.Hayter@du.edu;3. Department of Statistics, Chulalongkorn University, Bangkok, Thailand;4. S3RI and School of Mathematics, University of Southampton, Southampton, UK |
| 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. |
| Keywords: | Acceptance sets Confidence intervals Cumulative distribution function Non central t-distribution Normal distribution Simultaneous confidence level |