Abstract
To each positive definite probability density there exists an adjoint density which is proportional to the characteristic function of p. The products have a greatest lower bound Λ, and it is known that 0.5276… < Λ ≤ 0.8609… We present a positive definite density with λ(p) = 6/7 and thereby improve the upper estimate. For densities representable as normal scale mixtures, we show that λ(p) ≥ 1 with equality if and only if p is a normal probability density.
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