Non-symmetric Linnik distributions
Erdoğan, M. B.
Ostrovskii, I. V.
Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
511 - 516
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The aim of this Note is to study the probability density with characteristic function ρα,θ,v(t) = 1/(1 + e-iθsgnt|t|α)v, where 0 < α < 2, |θ| ≤ min(πα/2, π - πα/2), and v > 0. This density, first introduced by Linnik for θ = 0, v = 1, received several applications later. It does not have any explicit representation. We consider here its integral and series representations and its analytical properties.