A positive probability law has a density function of the general form Q(x) exp(−x1/λL(x)),
where Q is subject to growth restrictions, and L is slowly varying at infinity. This law
is determined by its moment sequence when λ < 2, and not determined when λ > 2. It
is still determined when λ = 2 and L(x) does not tend to zero too quickly. This paper
explores the consequences for the induced power and doubled laws, and for mixtures. The
proofs couple the Carleman and Krein criteria with elementary comparison arguments.
Australian & New Zealand Journal of Statistics 43(1), pp.101-111