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

Sanjib Basu

Statistics & Probability Letters, 1996, vol. 28, issue 2, 115-120

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

Keywords: 62E10; 60E05 Moment theory Normal scale mixtures (search for similar items in EconPapers)
Date: 1996
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0167-7152(95)00104-2
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:28:y:1996:i:2:p:115-120

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().