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Existence of a normal scale mixture with a given variance and a percentile

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  • Basu, Sanjib

Abstract

We consider the constrained normal scale mixture distribution family [Fourier transform](p, Q; [sigma]2) = F is a normal scale mixture and F(Q) = p, VarF(X) = [sigma]2. We show that [Fourier transform](p,Q; [sigma]2) is nonempty, i.e., a normal scale mixture distribution with 100p-th percentile at Q and variance = [sigma]2 exists if and only if p [greater-or-equal, slanted] a fixed constant. We next match the percentile Q with a normal percentile, QN = [sigma][Phi]-1(p). We prove that the class [Fourier transform](p, QN; [sigma]2) contains distributions other than N(0, [sigma]2) if and only if QN/[sigma] > 1.1906

Suggested Citation

  • Basu, Sanjib, 1996. "Existence of a normal scale mixture with a given variance and a percentile," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 115-120, June.
    • Handle: RePEc:eee:stapro:v:28:y:1996:i:2:p:115-120
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    Cited by:

    1. Xiang, Sijia & Yao, Weixin & Seo, Byungtae, 2016. "Semiparametric mixture: Continuous scale mixture approach," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 413-425.
    2. Sanjib Basu, 1999. "Conservatism of the z Confidence Interval Under Symmetric and Asymmetric Departures from Normality," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(2), pages 217-230, June.

    More about this item

    Keywords

    62E10; 60E05 Moment theory Normal scale mixtures;

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    Statistics

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