New Sufficient Conditions for Moment Determinacy via Probability Density Tails

Gwo Dong Lin () and Jordan M. Stoyanov ()
Additional contact information
Gwo Dong Lin: Institute of Statistical Science, Academia Sinica, Taipei 11529, Taiwan
Jordan M. Stoyanov: Institute of Mathematics & Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria

Mathematics, 2025, vol. 13, issue 16, 1-12

Abstract: One of the ways to characterize a probability distribution is to show that it is moment-determinate, uniquely determined by knowing all its moments. The uniqueness, in the absolutely continuous case, depends entirely on the behaviour of the tails of the probability density function f . We find and exploit a condition, (D), in terms only of f which is of a `general’ form and easy to check. Condition (D), showing the `speed’ for f to tend to zero, is sufficient to conclude the moment determinacy. We establish a series of theorems and corollaries in both Stieltjes and Hamburger cases and provide an interesting illustrative example. The results in this paper are either new or extend some recently published results.

Keywords: random variable; density; moments; moment determinacy; Stieltjes case; Hamburger case; Carleman’s condition; probability density tails; Gumbel distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/16/2671/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/16/2671/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:16:p:2671-:d:1727946

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().