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A note on the maximum deviation of the scale-contaminated normal to the best normal distribution |
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| Authors: | Dankmar Böhning Roumporn Ruangroj |
| Institution: | (1) Department of Epidemiology, Joint Center for Humanities and Health Sciences, Free University Berlin, Humboldt University at Berlin, Haus 562, Fabeckstr. 60-62, 14195 Berlin, Germany (E-Mail: boehning@zedat.fu-berlin.de), DE;(2) Department of Mathematics and Statistics, Faculty of Science and Technology, Thammassast University, Pathumthani, Thailand (E-Mail: roumporn@alpha.tu.ac.th), TH |
| Abstract: | In this paper we consider the case of the scale-contaminated normal (mixture of two normals with equal mean components but different component variances: (1−p)N(μ,σ2)+pN(μ,τ2) with σ and τ being non-negative and 0≤p≤1). Here is the scale error and p denotes the amount with which this error occurs. It's maximum deviation to the best normal distribution is studied and shown to be montone increasing with increasing scale error. A closed-form expression is derived for the proportion which maximizes the maximum deviation of the mixture of normals to the best normal distribution. Implications to power studies of tests for normality are pointed out. Received May 2001 |
| Keywords: | : mixture of normals with different component variances scale-contaminated normal maximum deviation suprenum's norm |
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