ON MIXTURE REPRESENTATION OF THE LINNIK DENSITY

Let p(alpha,theta) be the Linnik density, that is, the probability den sity with the characteristic function phi(alpha,theta)(t) := 1/(1 + e( 1 theta sgn t) \t\(alpha)), (alpha, theta) is an element of PD, PD := {(alpha, theta) : 0 < alpha < 2, \theta\ less than or equal to min(pi alpha/2, pi - pi alpha/2)}. The following problem is studied: Let (alp ha, theta), (beta, theta) be two points of PD. When is it possible to represent p(beta,theta) as a scale mixture of p(alpha,theta)? A subset of the admissible pairs (alpha, theta), (beta, theta) is described.