Theory & Methods
Criteria for the Unique Determination of Probability Distributions by Moments
Article first published online: 18 DEC 2002
Australian Statistical Publishing Association Inc. 2001
Australian & New Zealand Journal of Statistics
Volume 43, Issue 1, pages 101–111, March 2001
How to Cite
Pakes, A. G., Hung, W.-L. and Wu, J.-W. (2001), Criteria for the Unique Determination of Probability Distributions by Moments. Australian & New Zealand Journal of Statistics, 43: 101–111. doi: 10.1111/1467-842X.00158
- Issue published online: 28 JUN 2008
- Article first published online: 18 DEC 2002
- Cited By
- Carleman and Krein conditions;
- moment problem.
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.