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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 相似文献
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