Statistical distributions and the moment problem
Project funded by own resources
Project title Statistical distributions and the moment problem
Principal Investigator(s) Kleiber, Christian
Organisation / Research unit Departement Wirtschaftswissenschaften / Ökonometrie und Statistik (Kleiber)
Project start 01.10.2010
Probable end 31.12.2025
Status Active
Abstract

The moment problem asks whether or not a given probability distribution is uniquely determined by its moments. The existence of moment-indeterminate distributions has been known since the late 19th century; however, first examples were often considered as mere mathematical curiosities. Recent research has shown that the problem is more widespread than previously thought and also that it is relevant in more practical contexts. Specifically, distributions that are not determined by their moments arise in applied economics, notably the modelling of economic size distributions, and also in mathematical finance. The project investigates determinacy issues for selected distributions from these fields.  It will also consider the multivariate case, for which current knowledge is much more fragmentary than in the classical univariate setting.

The moment problem asks, for a given distribution with distribution function (d.f.) $F$ with finite moments $m_k (F) = \E[X^k] = \int x^k F(dx)$, $k = 1, 2, \dots,$ of all orders, whether or not $F$ is uniquely determined by the sequence $\{m_k(F), k \geq 1\}$for a given distribution with distribution function (d.f.) $F$ with finite moments $m_k (F) = \E[X^k] = \int x^k F(dx)$, $k = 1, 2, \dots,$ of all orders, whether or not $F$ is uniquely determined by the sequence $\{m_k(F), k \geq 1\}$.
Keywords moment problem, statistical distributions
Financed by University funds

### Published results ()

ID Autor(en) Titel ISSN / ISBN Erschienen in Art der Publikation
929269  Kleiber, Christian; Stoyanov, Jordan  Multivariate distributions and the moment problem  0047-259X  Journal of multivariate analysis  Publication: JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift)
1473749  Kleiber, Christian  The generalized lognormal distribution and the Stieltjes moment problem      Publication: Discussion paper / Internet publication
1544544  Kleiber, Christian  On moment indeterminacy of the Benini income distribution  0932-5026  Statistical Papers  Publication: JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift)
1544545  Kleiber, Christian  On moment indeterminacy of the Benini income distribution      Publication: Discussion paper / Internet publication
1473747  Kleiber, Christian  The generalized lognormal distribution and the Stieltjes moment problem  0894-9840  Journal of Theoretical Probability  Publication: JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift)

### Cooperations ()

ID Kreditinhaber Kooperationspartner Institution Laufzeit - von Laufzeit - bis
462470  Kleiber, Christian  Stoyanov, Jordan  Bulgarian Academy of Sciences  01.10.2010  31.12.2025

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