Journal of the Australian Mathematical Society - Series A Vol. 64 Part 3 (1998) On mixture representation of the Linnik density Burak Erdogan Department of Mathematics Bilkent University 06533 Bilkent Ankara Turkey e-mail: erdogan@fen.bilkent.edu.tr e-mail: iossif@fen.bilkent.edu.tr and I. V. Ostrovskii Abstract: Let $p_{\alpha,\theta}$ be the Linnik density, that is, the probability density with the characteristic function $$\begin{gather*}\varphi_{\alpha,\theta} (t) := 1/(1+e^{i\theta\sgn t}\vert t\vert... ...< 2, \vert\theta\vert\leq \min(\pi \alpha /2,\pi-\pi \alpha /2)\}. \end{gather*}$$ The following problem is studied: Let $(\alpha,\theta)$, $(\beta,\vartheta)$ be two points of PD. When is it possible to represent $p_{\beta,\vartheta}$ as a scale mixture of $p_{\alpha,\theta}$? A subset of the admissible pairs $(\alpha,\theta)$, $(\beta,\vartheta)$ is described. PDF file size: 52K © Copyright 1998, Australian Mathematical Society