On mixture representation of the Linnik density

Burak Erdoǧan, I. V. Ostrovskii

Research output: Contribution to journalArticlepeer-review

Abstract

Let pα,θ be the Linnik density, that is, the probability density with the characteristic function φα,θ(t) := 1/(1+eiθsgnt|t|α), (α,θ) ∈ P D, P D := {(α, θ) : 0 < α < 2, |θ| ≤ min(πα/2, π - πα/2)}. The following problem is studied: Let (α, θ), (β, θ) be two points of P D. When is it possible to represent pβ,θ as a scale mixture of pαθ? A subset of the admissible pairs (α, θ), (β, θ) is described.

Original languageEnglish (US)
Pages (from-to)317-326
Number of pages10
JournalJournal of the Australian Mathematical Society
Volume64
Issue number3
StatePublished - Jun 1998
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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