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Krein condition in probabilistic moment problems. (English) Zbl 0971.60017

This paper makes an extensive use of the well-known Krein and Lin conditions [which are integral tests on the density function, see e.g. G. D. Lin, Stat. Probab. Lett. 35, No. 1, 85-90 (1997; Zbl 0904.62021)], to prove the M-determinacy or the M-indeterminacy of powers of the log-normal, normal, and inverse Gaussian distribution. As in previous papers [C. Berg, Ann. Probab. 16, No. 2, 910-913 (1988; Zbl 0645.60018) and G. D. Lin and J. S. Huang, Aust. J. Stat. 39, No. 3, 247-252 (1997; Zbl 0898.62015)], the cube appears to be the frontier from which the powers of the latter distributions become M-indeterminate. There is also a conjecture concerning the classes of functions preserving or destroying the M-determinacy.

MSC:

60E99 Distribution theory
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